Can I tune a rig to 75ohms? Is there a downside to this ?

There's no problem whatsoever. You'll have to get hold of (or build) a 75Ω dummy load and SWR / power meter. I used to build all my UHF gear to match 75Ω so I could use TV coax, 75Ω BNC connectors and 75Ω TV aerials.

Will a 50ohm power meter show a mismatch ?

Probably not depending on the meter, the coupler in the meter would be 50R however it would be too short to cause any mismatch worth worrying about - however one thing, it would most likely give you an inaccurate power reading because of the difference in impedance. At 75R you’ve got slightly more RF voltage and less current (ohms law), so the rectifier diodes in the meter will produce a higher DC output resulting in an increased power reading.

Conveniently, 1 Watt at 12V supply gives a 72Ω match which is actually the real characteristic impedance of most of the TV aerials and feeders. My little link rigs at ~540MHz used a pair of grounded base 2N3866s for 1 Watt output into 72Ω. The PA ran pretty cool, and it was dead easy to calibrate the output filter since the input impedance and the output load impedance were exactly the same. I used "Lecher Bars" for the output filter inductors, with small surface-mounted capacitors soldered between them and ground at strategic points.