Can I tell from one particle of an entangled pair whether the other particle has been observed? I want to ask about a pair of entangled particles, each one heading towards a different group of experimenters.
When one group observes their particle, is it possible for them to tell whether the other group had observed their particle at that point?
 A: No.  The relative probabilities of the observables will be exactly the same as they would have been if the other entangled particle hadn't been observed, it's just that if you later compare the measurements on the two entangled particles, you will find that the measurements are correlated.
Edit (in response to Norbert's comment):  In fact, the measurements will be correlated in a way that would be impossible with classical particles without faster than light signaling.  But the fact remains that nothing you observe about one particle will indicate whether the other particle has been observed.
A: 
When one side of an entangled pair is observed [...]

Whether and in which way a pair had been entangled can of course only be known from both having been observed, and both observations having been (separately) evaluated and the results having been correlated.

Is it possible for that side to detect or infer whether or not the other side was already observed at that point?

Considering only one side of a pair there cannot be made any inferences about "the other"; it cannot even be inferred whether or not some particular "other side" might have been "in play" at all.
But it is certainly possible for one side to detect the other side having broadcast their results, before collecting observations pertaining to the own ("one") side of the pair. If so, the two events to which the observations belonged were time-like related to each other. 
A: No, but if there are only two possibilities they will know what the other measurement will be.
