Funny that no one else mentioned it so far, and perhaps not the silliest mistake a noob like me could do, but it was certainly one of the first mistakes:
Trying to push back the A320neo with parking brakes still on - and wondering why this takes like forever!
A classic 
Following the instructions of the in-game ATC. Got me crashed a few times. It was fun though.
My silliest mistake was not using the MSFS check sheet. Landed wheels up.
I actually witnessed the same scenario at my flight school years ago with a fellow trainee.
He landed wheels up and his instructor was in the co-pilot’s seat … go figure…smile
Oh yes, for real and horrible damage to the aircraft underbelly , prop and engine.
Plenty of silly mistakes, but most recent (Friday?): flew the PMDG 737-800 from KDEN to KMCO. This plane has a “pause before TOD” feature, which is great for long flights when you go do other things in the house while at cruise altitude. Unpaused, started descent, FMS speeds seemed really off. Then the low fuel light warning went on. Turns out the entire flight was with Flaps 1 set. There’s like 10 flap settings in this plane, and I failed to hit my flap switch that last time. Still landed fine with like 800 lbs of fuel left, which is about the amount you want left on a business jet, but wayyy below an airliner reserve. My new SoP…hit the flaps up lever several times at climb, just to make sure they’re fully retracted. 
Wondering why I can’t get any speed ten minutes after takeoff, switching to external view, realizing your flaps and gear are still hanging out in the wind…
Forgetting to put the prop lever full forward for takeoff -
Forgot to turn off the APU after engine start and took off with it running.
Was distracted during checklist.
Forgetting to turn off apu before takeoff.
Well I finally made a silly mistake. I was at an airport using the pushback toolbar to manually push me. Normally I preplan the pushback and let it do so automatically. I’m also usually at an airport with visible ground crew. Not this time.
This time there was no visible pushback dolly even though I was still able to perform the pushback. When I was done, I hit the hold button, got distracted and thought the dolly went back to the starting position, hit the throttle… And didn’t move. Parking brake off, check. Full throttle? Still no movement.
Turns out the hold option for the pushback toolbar is a temp hold, and doesn’t release the plane. I was still held in place by the invisible dolly until I cancelled the pushback. Those are some stout little dudes!
first flight in the Twotter I mistakenly set the wing tip tanks to feed direct to engines instead of into the main tank. Then, when the engines died while cruising at only 2,500’ even tho I realized why and switched to main tanks before restarting, I didn’t pull back the power levers so when the first engine came back to life at full power it put me into a spin that I couldn’t recover from before getting the other engine back up. RIP
I’ve made every mistake under the sun tbh. Probably the most funny was when I’d organised a bush flight with some peeps on discord. Anyway, I’m feeling happy to have finally of got a bush flight going but I was climbing out and really struggling to keep pace.
After much faffing around and all of us trying to troubleshoot my issue, beginning to the think the game was bugged, I realised that I was still full rich @ 9000ft in a little cub (high terrain). Oops.
Landing without landing gear in CRJ, it was so smooth it didn’t even register as a crash just slid to a halt on the runway and that was it lol (controlled slide with small rudder inputs)
Not going around when I should have done and ending up with a crash. Too many times to remember!
Forgetting I have a boom mic on and then trying to eat/ drink…
…Yoghurt is the worst … 
Another one: started flying the Beech Bonanza, which is pretty good for a stock plane. Until on a couple of longish flights but well within the theoretical range, the engine just seemed to stop, even though it showed it had plenty of fuel. I of course assumed that the plane was a piece of junk. Then I started looking harder, realized there are two fuel gauges, and figured out that the L and R fuel tanks don’t auto-balance You have to switch tanks every few minutes to balance them, using a switch hidden on the floor. Then it went back to being an excellent airplane.
Oh jeez. Forgetting to put the gear up (thankfully not down, yet.) Overspeeding the C208 on descent before I learned about FLC on the G1000, forgetting to check my fuel and therefore making another artificial reef in the ocean, etc.
I’m glad it’s all virtual!
Been there, done that
I was landing in Toronto, Canada. On Final Approach with the B777-300, was a very cold cloudy night. All of a sudden I was losing airspeed and started losing altitude rapidly, I crashed hard before reaching the runway. Completely forgot to put the anti-ice on, I always remember to activate it now lol
Forgot to check my fuel before I took off and ran out a mile short of the runway. Didn’t end well.
I had an issue similar to that once. I finished my pushback, and after checking my lights, released parking brake and tried to start my taxi, but it didn’t matter how far I pushed my throttle the aircraft refused to move or it did it very, very slowly even at TO/GA!!
I finally discovered I forgot to disconnect the pushback tug 