You're basically looking for two things: first, an abrupt stop to frequencies above a certain point -- compression uses applies a low-pass filter to eliminate them.

Second, a bunch of rectangular-ish boxes where signal is missing. The spectrogram will look like swiss cheese in a way -- this is where the compression algorithm decides audio information can be deleted because it's "masked" by e.g. louder surrounding sounds.

(Generally speaking, the more aggressive the compression, the lower the frequency ceiling, and the more/bigger swiss cheese holes.)

On the other hand, if you run e.g. AAC compression at a very high bitrate and explicitly force no lowpass filter at all (which virtually nobody does in practice, but you can do from a command-line tool)... you won't be able to see any qualitative difference. Because you won't be able to hear any qualitative difference either. :)

I imagine low pass filtering depends a bit on which compression you're using.

None of these tricks will work for detecting GAN compressed audio, though.

http://tausoft.org/wiki/aucdtect

I wonder if there is any open source implementation of the algorithm it uses.

http://tausoft.org/wiki/True_Audio_Checker_Algorithm

I'm guessing sometimes frequency cutoff is due to using less than ideal microphones, although not the extreme cutoffs (I'm fairly sure it would be gradual in that case). It also seems there is often a fair amount of noise around 20kHz that I'm guessing is from recording equipment, sometimes on tracks that otherwise look suspiciously like they are from lossy audio. Additionally, in some cases there could potentially be high frequency cutoffs in processing while otherwise being lossless, particularly stuff like electronic music where there can be a lot of processing in general. So I'm not sure if it is necessarily all that easy to tell in general, although there are certainly some from Bandcamp that seem highly likely to be conversions from lossy formats :(.