following is a chart of potential mower carburetor problems.
. erratic idol
you could have a vacuum leak try partially restricting air flow to carburetor if idle smooths out look for damaged intake gaskets
. hard to start after engine is at operating temperature
you could have a valve adjustment issue check owners manual for correct settings
a vacuum leak could have the same affect, do a visual check of all gaskets intake ect.
Engine will not start
Engine hunts (at idle or high speed)
If your sure you have fuel check for fuel delivery some small engines have fuel pumps that can fail.
engine runs but has black exhaust
Check for bent choke and throttle plates
check for intake obstruction such as dirty air filter.
. you have fuel but your mower will not start
Adjust control cable or linage, to assure full choke and carburetor control also you could have a stuck needle and seat in the float bowl this may not be something you want to tackle with out some knowledge of carburetors.
. general poor performance
start with the most simple solutions first such as old fuel or it may be time for a tune up or a clogged air filter ect. keep it simple .