The idea I get from both usage and dictionaries is that 一応 is typically used when someone or something is not ideal, but is good enough to deal with the task at hand, or is at the very least better than nothing: 「一応出来ました」 (It's finished, but I'm not confident of the quality). It can also be used when you're not sure something is necessary, but do it anyway just in case: 「一応傘を持って行く」 (I'll take an umbrella with me even though I'm not sure I'll actually need it). The key seems to be uncertainty in whether or not what you're commening on will actually be useful or relevant. The fact as presented is a fact, but there may not be any point to it.
So here are some examples, all from Ar tonelico 2 since I happen to have a lot of text from that handy.
- (Croix, when the party needs to continue on but one of the characters went off alone and hasn't returned) 「一応書き置きだけして、先に行こう。」 "Let's at least leave a note before we move on." (She may never see it, but hey, at least we tried, right?)
- (Skycat, after the party misuses the restaurant where she works as a supply shop and item factory too many times) 「たまには何か食べて行ったらどうなの？一応うちってレストランなのよね。」 "Why don't you eat something once in a while when you're here? This is a restaurant, for what it's worth." (Not that you seem to care, but it really is.)
- (Sasha, when presenting an unknown recipe card) 「一応レシピはあるので、作ることは可能ですが…。」 "There's a recipe, anyway, so you should be able to make something..." (I have no idea what it makes, or whether it's worth the trouble, but there's a recipe there regardless.)
- (Cloche, after using magic to heal a wounded child) 「この子、足を怪我してました。回復魔法は掛けておきましたが、一応薬屋へ。」 "This child injured his leg. I've used healing magic on it, but visit the pharmacy just in case." (The magic should have been enough, but it's better to be safe than sorry.)
- (Luca, in one of the Cosmosphere school settings) 「一応、ここはね、そこそこ頭のいい進学校なんだよ～。」 "This place is supposed to a pretty brainy college-bound school, after all." (At least in theory. It's noted elsewhere in the scenario that only one or two students actually seem to understand the coursework.)
- (Kurokaki, when Fururu gets sidetracked) 「一応仕事中なんだぞ？」 "Hey, we're supposed to be on the job." (Maybe it doesn't make that much difference that we're working, but we should at least make a token attempt to be responsible and stay focused.)
Besides the brief but not always applicable "technically", possible corresponding phrases may include "for what it's worth", "such as it is", "on paper", "more or less", or "in a sense" when it's being used to indicate that a description may not be entirely adequate or relevant. For the case where something might not be necessary, "just in case" and "to be on the safe side" tend to work well.
It may help to note that 一応 was originally written 一往, which literally translates to "one journey". Perhaps the typical modern meaning relates to the idea of not being able to fully experience a destination in only a single visit, so you're effectively saying your understanding of the situation is incomplete.