Using AC fuse for DC & DC fuse for AC...!
I would be worried if it's the other way around because the DC arc is not self-extinguishing like the AC one is at the zero crossing. Trying to be cheap with fuses at one point I realized that even a 0.3A AC fuse can glow for a couple of seconds on DC... And this was 250V AC rated fuse and I was only using at 12V DC.

For an inverter, if the electronics fail short to the DC rail somehow and it "decides" to output DC... I'd be glad the fuse was DC-rated (as long as it's not under-rated in terms of AC voltage).