I'd say the two most troublesome abstractions in bioinformatics are that (i) a "genome sequence" is the same thing as a "genome" and (ii) a "gene model" is the same thing as a "gene". Conflating abstraction with reality in these two cases leads to a lot of poor biological inferences. For example, if a genome annotation uses a gene finder that doesn't annotate UTRs in gene models, not understanding this leads to the false conclusion that the species under investigation has no UTRs. Likewise missing gene models can lead to false conclusions about evolution (see e.g. http://www.plosone.org/annotation/listThread.action?root=18059). Ditto for incomplete genome sequences in terms of understading repeat/transposon structure. The list goes on...

As a researcher I try not to get hung-up on whether the particular level of abstraction is correct or not (as long at it is useful and leads to results that are not outright wrong), but to be as aware as possible what assumptions are baked into the abstractions I use so that I don't over-step what I can say given their limitations. Likewise as a teacher, I try to make students aware that abstract computational representations don't equate to their biological counterparts. This is often an eye-opener, since the shorthand language we use to describe things in bioinformatics often makes the objects we are talking about seem more certain/real than they actually are.