Nope, you're all good. The one thing to watch out for is that you cannot revert a savegame if you later decide you want to -- so hang on to a copy of the original save if you think you want to. But savegames are always forward compatible, and I routinely test this with saves from pre-1.0 (before the game was even out), the 1.013 range, the 2.0 range, and then the post 3.0 range.
When upgrading from some of the really distantly far back versions, there are of course a few hiccups that are unavoidable. The balance might be skewed from what it would have been, for instance: reinforcements higher or lower than they should be, or other things in concentrations the should not be, etc. But even with the really really old saves, the game detects the worst of those and does things like adding in extra capturables as needed, scrubbing out the most egregious excesses of things that should not be in too many concentrations in the hands of the AI, etc.
There are also some collision issues when you go that far back, based on things like command stations, space docks, and energy reactors now being much larger. They tend to really overlap one another when loading a savegame from that far back, which looks bad but which does not affect gameplay. For the AI ships that would have that issue, we automatically correct that on load, but for players that has other consequences (making force fields no longer sufficient, etc), and so we don't do any auto-correction at all for player ships there, letting players themselves autocorrect if they so desire.
None of that at all applies for moving from 3.060 to 3.100 or similar (or even 3.000 to these betas), but I figured I would give an all-inclusive answer since others may have older savegames that they are wondering this about. The upgrades-in-the-middle can definitely alter the flow of a game as older strategies get nerfed and new ones become available, etc, but that's not something that is breaking in a literal sense (it could mean that you now lose where you might have won before, or vice-versa, but even that is pretty rare).
Forward compatibility is super important to us, so we put a lot of effort into making sure that it "just works" in every case that is feasible.
EDIT: Ninja Keith strikes, this time, and beats Ninja Chris to it.
