XXLHardrock

Is it realistic to expect full, noiseless use of a 10 speed cassete in either chainring (50/34) as long as the trim function is working properly?

Also, the Shimano set up instructions focus on getting the trim to work from small to large chainring but don't say much about going the other way.

trailflow1

On my 10 speed Dura Ace 7900 there is only a trim on the small ring. When on the big ring the FD cage is wide enough to use all 10 gears when if adjusted correctly. Setting the correct height and angle of the FD is crucial and can take a few attempts.

i don't have any experience of 105 10 speed but im guessing it functions the same way as DA.

You should also check your chainline. You might have too many spacers on the bottom bracket on the drive side. That is pushing the crank too far out.

If you have a small sized frame with a short wheelbase and chainstays. The chain angle can be more extreme when using big/big or small/small.

Dyskolos

I am using a 10-speed 105 group on a compact front and, yes, it is noiseless in all combinations when adjusted properly.

Andrew R Stewart 

Rubless chain run does depend on both matching the components as well as proper chain line (which is independent of the parts in use). Andy.

Yellowbeard

It's possible, but your chain may still rub against the side of the large ring when in small-small gears. Mine does in the two smallest cogs, at least.