Does the FAA or FSS check or authorise IFR flight plans?
The FAA's flight plan filing FAQ says that it's about formatting:


  Q: Will an FPL be automatically rejected or is that a manual function?
  
  A: ERAS automatically rejects an improperly formatted FPL. The Rejection (REJ) message usually includes information which identifies
  the error. The filer should correct the error and reenter the FPL.


That seems to be confirmed in this FAA ICAO Flight Planning Interface Reference Guide that goes into detail on computerized flight plan formats, filing etc. Section 3.7.2 lists all the possible reasons for the ERAS computer to return a REJ (rejected) message, and they're all to do with formatting or invalid values, e.g. airspeed can't be zero.

To me, that makes sense: no one knows the equipment or capabilities of an aircraft except the person (or organization) submitting the flight plan. Even if the FAA had a database of every aircraft in the world, what happens if your GPS unit burns out and you want to file IFR using only standard IFR equipment (VOR, ILS)? Or you want to fly at a reduced (or increased) cruise speed for some mechanical or performance testing reason? The FAA couldn't possibly know if your submitted values are correct.

I don't know (and couldn't find out) if there's any situation where ERAM can't generate a flight strip even though the flight plan is accepted as valid. If it does happen, I suppose that would be a sort of secondary check.

As an aside, I was at an EAA IMC Club meeting last week and we discussed the new ICAO flight plan format (new to the US, that is!). A couple of controllers were there, and they said that you have to be careful about what equipment you put in your flight plan in case you get assigned something beyond the pilot's capabilities. For example, a Cirrus is PBN-capable and if you input all the equipment correctly in the flight plan then you may get a complex SID rather than just departure vectors. If you aren't familiar and comfortable with the avionics then you might get yourself in trouble, so it would be better to file only basic avionics. That kind of decision isn't something the FAA could or should validate.