Known problems with IIR DF2 when using 64-bit floating point processing?
Depends on how close your poles are to the unit circle. For DF2, the transfer function from the input to the state variables are given by the poles, so there can be substantial gains in there. For typical audio filters, it's not unusual to see 100+ dB of gain and that would definitely be a problem for 32-bit floating point. 

These enormous gains also make updating the filters dynamically very tricky since it will typically generate massive transients. 

I suggest looking at transposed form 2. It's often as efficient as DF2 but has  much better behaved state variables.