No idea what a MTD 820 is,but are you refering to a manual gearbox,or a "hydro"??I always look into my manual under tranmision,for the particular unit in qestion.. JMHO tbk

If going into gear, you have to hold it toward the range you want, then let up on the pedal slightly, then it
clicks in, I would not worry too much.
Does it click into these positions easily when the engine is off?, if so, the belt may be slightly turning the trans pulley. Make sure you have the correct belts.
Has this problem just started?

Fish

MTD 820 manual (but you can increase forward drive speeds while in motion).

Engine on/off makes no difference to the behavior it seems and the problem just recently cropped up.

Before it used to slide into position effortlessly now it requires a slight tap and when coming out of a position , it almost seems to be binding on something.

Visually inspected and all it is is a rod that goes into the transmission housing and it isn't binding on anything I can see.

On transmissions, there usually is a couple of set screws, allen headed, that can be removed, and underneath
there are springs, and under the spring, is a ball bearing
They are called detent balls and keep the shifted "clicked"
into the spot they need to be. Try removing them and inspecting them, if you see a lot of rust, then that would be your problem, you might be able to add some lubricant
drops in the holes and it may help.

I too have no clue what a MTD 820 is? But, if it has a drive belt to the transmission I would make sure it's not cracked, worn out, or have burned spots. I would also look an the idler pulley and linkage before I would open up the transmission.

It has a high/low range and reverse, and a seperate lever for the speed selection, but the standard variable speed
double belt/pulley setup.

Fish