Neither spell requires that you maintain concentration to keep the spell in effect. By that it would appear that in neither case would the caster begin to fall as a result of the spell no longer being in effect. For example, a caster under levitate can be pushed, pulled and dragged in any direction by other forces and if released the spell will maintain them in their current position and height.
As a DM, however, I might rule in the case of Levitation that you would be considered off-balance, as if you were engaged in melee combat. This causes a penalty each round until you take a round to stabilize yourself. I think that would depend on the situation (i.e are you using Shift to evade a melee attack mid-air).
Further, for the Fly spell I would probably at least make you roll a fly skill check to overcome any possible disorientation from suddenly flying along a different path than before.
Other than that, I see nothing in any of the descriptions that would cause any issues with you employing this tactic.
As for your first question, there is nothing in the Dimension Door spell that indicates that your destination has to be on ground. It states any other spot within range. So I would say that mid-air is perfectly justifiable as "a nearby space".