Two suggestions:
Make sure you have set the jumper for the Picasso's memory to either use segmented or unsegmented (recommended).
You may also want to install enforcer as there may be conflicts between the 68020/30 caches and ZII memory accesses to the Picasso board.
If you're using an old Zorro II memory board you may want to make sure the dram chips on it are at least as fast or nearly as those on the Picasso; if there's a wide discrepancy between the speed rating (e.g. 150ns on the ZII memory board and 80ns on the Picasso) you could be asking for trouble. Generally, I've had no problem with 100ns drams on a ZII board and 70 or 80ns on the Picasso II. It's worth a shot.
And also make sure all those dram chips on any memory board, including the Picasso are seated properly. You could even try reseating the ones on the Picasso in case there's a bad contact.