The main problem has always been vibrations from the compressor. The simplest way to avoid this is to have the compressor located as far as possible from the cryostat and to connect the two using tubes that do not transmit vibrations well, Where I work we generally try to keep the compressors in another room if possible (in one case it is actually in a room on the other side of the corridor).
The second problem has been electrical noise from the pumps. Grounding etc is very tricky but some of the manufacturers claim to have solved that problem in the latest generations of dry (dry=cryogen free) fridges; at a conference a few months ago I even saw a dry dilution fridge with a turbo mounted on top of the fridge (I think it was the VeriCold design now sold by Oxford Instruments); the manufacturer claimed that there shouldn't be any problems with either mechanical nor electrical noise (although I am not sure I believe them).
Note that single stage coolers are a mature technology now, if you only want to reach temperatures of about 20K or so vibrations should not be an issue. It gets a bit trickier with two-stage coolers that can reach 4K and sub-1K fridges (He3 and dilution fridges).