I have a 200Mhz oscilloscope and I'm seeing some strange signals in FFT mode at 25Ghz with peaks at 12.5 and 37.5 respectively. There are definitely peaks at those frequencies, they appear, stay on for several 10s of seconds and then occasionally vanish. I've also seen stuff fluttering around in the 2.4 GHz range before, is this a bug or are there MMW signals in my room? Is my scope oversampling, and if so by how much? 
Your scope (if it is same as in your some previous message in EEVblog), Hantek 5202P have maximum real time sampling speed 1GSa/s (and it is also done using multiple ADC's interleaved.
Maximum theoretical FFT is 500MHz (fNyquist)
In this mode, if FFT frequency band go over 500MHz is totally designer error.
But then it have also Equal Time Sampling mode. I do not remember if ETS max is "25GSa/s" or "50GSa/s"
Is it so that FFT can also enable when in ETS mode? If so, then..
If it have max ETS 50GSa/s then FFT is 0-25GHz based to sample speed. In theory and practice it can work but it need extremely good "nearly ideal" timing and so on. And in this Hantek, this is not at all - nearly worst possible. Sampling quality is totally junk for this purpose and also its analog front end can not handle these higher frequencies, so thes what you see are not from outside of scope.
But, it must say, what ever 20GHz or something like it you can see there, they are total bullshit, generated by sampling system and FFT math itself. Think there is many separate ADC very poorly interleaved, Then in ETS mode these acquisitions are repeated many many times. How are they positioned and are there really picoseconds class real timing accuracy. Really not, not at all. There is ADC clock's jitter and also levels are not well balanced between adc's, there is trigger jitter etc. In real world these samples are shot like a shotgun. After then they are arranged like they are in line at regular intervals. FFT math input data is garbage and result is garbage^k
Then more, afaik it have 1k sample points for FFT math.
About ETS sampling and FFT:
http://literature.cdn.keysight.com/litweb/pdf/5988-4368EN.pdfand there page 16
Also FFT without Equal Time Sampling mode is problematic because partially same reason. Many interleaved ADC with poor timing and level balancing.
But, of course it can use and it is much more than no FFT at all. But user need understand its limits for avoid confusion between true world and scope display.