What’s the best way to make money in Tiny Tower

UPDATED: I wasn't really satisfied that my previous answer was correct, so I spent some time experimenting. I was partly right and partly wrong.

Experiment 1:

• I traversed the 1st island with the screen pressed nonstop. It took approximately 60 seconds for the day/night division line to move from 90° (vertical) to approximately 20°.
• I traversed the 2nd island with the screen pressed nonstop. It took approximately 35-40 seconds for the day/night division line to move from 90° (vertical) to approximately 20°.
• I traversed the 3rd island with the screen pressed nonstop. It took approximately 30 seconds for the day/night division line to move from 90° (vertical) to approximately 20°.
• Conclusion: The sun goes down progressively faster on each island.

Experiment 2:

• I performed Experiment 1 with a nest multiplier of x0 and x23. Results were extremely similar.
• Conclusion: Nest level does not appear to affect the speed of the sun.

Experiment 3:

• I went off the island 1 to island 2 jump at minimum speed. The sun went backward approximately 70°.
• I went off the island 2 to island 3 jump at minimum speed. The sun went backward approximately 35°.
• Conclusion: End of island jumps push back the sun, regardless of speed. These boosts diminish on each consecutive island (and appear to be gone completely by the 3rd or 4th jump.)

Experiment 4:

• I traversed nearly all of island 1 in fever mode. The sun moved backward approximately 10-20°.
• Tried slides, cloud touches and coin collecting. None of these activities, individually, appeared to have any effect on the sun.
• I deleted and reinstalled the game for Experiment 2, and I noticed that I was able to get to mid-island 7 pretty consistently, regardless of my much lower nest multiplier (and total score). So it appears that speed, not points, cause the sun to roll back or slow down.
• Conclusion: Going fast can push back the sun. Slides and cloud touches don't seem to have a major effect on the sun, although these are tied up with speed. This speed effect may also diminish on later islands, or it may simply be countered by the sun setting faster.
• Bonus Conclusion: There is a limit to how far the sun can be rolled back, about 90° backward from the starting position (with the sun just beyond the left edge of the screen).

The great things about bitizens is that they never seem to need to sleep. Thankfully you don't have to manage your bitizens personal concerns in this game, as the focus is the tower. Your bitizens will work 24/7 without any loss of productivity, so long as you can keep your shops stocked. So, yes, shops should be open at all times.

If you see them complaining in the Bitbook, I think that's just the developers way of adding some personality into the game. :) The only way to make a bitizen happy in the game is to employ them in their dream job. Failing that, until their dream job opens in your tower, best practice is to match them with the area that they are highest in according to their profile. They will at least remain content until such time as their dream job opens and you reassign them. So long as you can match them with a job of interest level 5 or greater, they will be content. Anything less than 5 and they will be unhappy in their job.