It is a somewhat disappointing that there is so little innovation in computer keyboard design--at least for lower-priced keyboards. In thinking about a better keyboard, I think one significant improvement would be a grid (a.k.a. matrix, rows and columns, non-staggered) layout. While it is not clear to me that such a layout would have significantly better finger movement properties--I have seen at least one claim to that effect, but that claim did not take into account the curve of the hand, only measuring physical distance--, it seems that such could have some nice mnemonic features.
In particular, one could overlay a number/navigation pad onto the main key space using the equivalent of a capslock to activate. The main benefit of such would seem to be not the reduction of movement per se but the reduction of context switching. Even if one can transfer one's hand to a separate number/navigation pad without looking, a bit more attention must be given to the transition compared to pressing a mode key. (One of the problems I have with vi[m] is that the default direction keys are not "intuitive"; a better mapping using the right hand might be: index finger, left, middle finger, down, ring finger, right, row-above-middle-finger, up.)
In addition to a grid layout, it seems appropriate to have a center section with specialized keys. Besides providing a more ergonomic separation of hands during typical use, such might also be more friendly to visual examination (not only would one's hands not block line-of-sight but they might also provide a visual framing context), which may be more common for less frequently used keys, and might be more friendly for from-and-back hand movement than placing such keys to the sides (the strong fingers are near the inside, inward arm movements might be slightly easier) and would seem be be better than placing such keys farther up on the keyboard (again, strong-fingers bias and possibly friendlier hand movement).
Of course, a laptop might have a problem with widening the keyboard, even with widescreen displays. A laptop would also favor a lower width-to-height aspect ration in the keyboard; desktop keyboards tend to have a higher aspect ratio than displays have. This issue requires some additional thought.
In addition to the above, the QWERTY layout is broadly condemned as substantially sub-optimal. However, the Dvorak layout that some promote also seems a little sub-optimal to me even at a cursory examination. E.g., the 'h' and 't' keys are on the right and left of each other when a common English two-character sequences is 'th' and "rolling" the right hand clockwise seems likely to be easier. (It is understandable that this would not be a consideration in the original design since Dvorak was designed for manual typewriters not keyboards. The placement of vowels might have a similar "rolling unfriendly" nature, the benefit of use-frequency placement might dominate. [Interestingly, I found the following quote on a site supporting Dvorak: "When the same hand has to be used for more than one letter in a row (e.g., the common t-h), it is designed not only to use different fingers when possible (to make keying quicker and easier), but also to progress from the outer fingers to the inner fingers ("inboard stroke flow") -- it's easier to drum your fingers this way (try it on the tabletop)." Now I have to think if "drumming" is more appropriate than "rolling" even on a keyboard--and with a more comfortable separation of hands rolling might be even less natural.) In addition, the arrangement of symbol characters seems likely to be sub-optimal for modern uses--especially for programmers.
Somewhat related to layout, a separated grid keyboard might be more friendly to internationalization in that it would be designed to a more common feature (the traits of the human body--variations in hand width, finger length, and other factors are issues with any layout), though a language with a higher count of commonly used glyphs might prefer more keys (that are harder to use) rather than requiring modes or digraph-like operations. Even so, it might be slightly easier to extend a grid layout without conceptual discord since a grid is so regular.
Another small issue I have with conventional keyboards is the relative lack of use of thumbs. While having the space key used by thumbs seems good, it seems it might be more appropriate to have separate keys for left and right hands (effectively required for a separated grid layout) and allow modifier keys to be used with the space key. E.g., it might be appropriate for shift-right_space to map to tab and shift-left_space to map to back tab; it might also make sense for the underscore glyph to map to a modified space--such seems to have a mnemonic appropriateness. While thumbs might only be able to use two keys where most fingers can somewhat easily reach three or more keys--and they may have to be oversized keys--, this would still seem to enhance the interface with the hands. (An alternative to keys might be a trackpad for gesture-based input. I have not learned to use a trackpad in place of a mouse, having difficulty with fine control of movement, but simple gestures such as slide up or slide down, with rapid repetition and motion speed variants as well as press and possible press-hop-press could be simple and coarse enough for common use.)
It also seems that there might be some opportunities to improve the "mnemonic sense" of the layout, though ergonomic factors should probably have priority. E.g., '!' might fit better as a shifted '.' In a similar manner, mapping the function keys to shifted--or otherwise modified--numbers might be appropriate. (Of course, this would break compatibility with having twelve function keys and with full flexibility in applying modifiers to such keys, but this might be an acceptable sacrifice for most people, especially since it could also make the function keys more accessible. This would also require finding suitable mappings for the symbol keys typically mapped to shifted numbers.)
In terms of learning a keyboard layout, as well as avoiding and recognizing mistakes, it is not clear whether "associated" or visually similar glyphs (e.g., 's' and 'z', 'm' and 'n'), should be placed close together or be widely separated. Proximity would seem to more easily allow a hunt-and-peck typist to see the alternate glyph (helping to avoiding typing the wrong key and perhaps guiding vision toward the correct key--seeing something that looks like the desired glyph drawing focus to the area which might then see the correct glyph) and might have some mnemonic value in learning to touch type. (The Dvorak placement of the vowels might have a mnemonic benefit as well as an alternating hand benefit.) Horizontally adjacent placement of opening and closing symbols might be more appropriate than symmetry based on left and right hands. While symmetric placement would balance hand use, the temporal separation of opening and closing would tend to make that immaterial--except in evil languages that force the programmer to use '()' (such an unbearable inconvenience! :-).
At the software level, an argument could be made that different types of key presses could have different meaning, particularly for mode setting keys. E.g., a double-press of shift might be an effective mechanism for setting capslock; it has a mnemonic advantage of using the shift key and avoids the need for a separate key for a relatively infrequently used function. Along similar lines, press-and-hold of a mode key might indicate that the mode should only be maintained while the mode key is held; press-and-release could then be used to indicate a persistent mode change. Unfortunately, this could have issues when another key is pressed while the mode key is still depressed; this would be interpreted as a single-key mode duration when the user might have intended persistence. Forcing the user to pause to account for the computer's inadequacies is inappropriate.
Many of the above thoughts are not unique to me (though the thoughts came to me before I saw that others had already discovered them). E.g., one person built a custom keyboard with several of the above features, and the "Truly Ergonomic Keyboard" has similarities (though it uses a presumably more expensive to manufacture slanted and wavey grid).
Another point that is sometimes made with respect to keyboard design is the lack of independent switching. I am not convinced that the cost of supporting such is worth the benefit. On the other hand, with a separated grid layout, it might be practical in terms of manufacturing and usability to provide more simultaneously distinguishable key presses that are from different hands. I have not even begun to think about trade-offs in that area.