In addition to the compatibility problems and the data recovery problems mentioned in the other answers, there is one inherent problem with the disk compression schemes:
They are sometimes quite off from the efficiency promise they offer.
The promise is that the added time for decompressing a file is somewhat offset by the reduced time for reading the now-smaller file from disk. One can even expect an overall speedup if the disk is slow and the CPU is fast. So far, so good.
On the other hand, if one tries random access to a file (i.e. not reading it as a whole from the start to the end) the promise somewhat breaks apart.
Writing is not quite as fast either. In contrast, for a non-compressed filesystem, writing is almost as fast as reading.
And things go really, really bad if one tries random-writing in a file (e.g. a database-like workload). The usual result is that the random write in a file is either impressively slow (100x is not unusual), or the file grows larger than the real data contained inside, or both, depending on the particular compression scheme used.
Then, there is the issue of completely arbitrary reporting of the free space available. Some software actually used these numbers and failed when they were inflated too much.