The most common problem is that the motor won't start at all.
My experience has been dirty points as the first place to check.
This page is for TD-20 and TN series motors, but shows in general how to check for spark.
Next step to checking/cleaning the points is removal of the flywheel.
Though not necessary to disassemble, you may find it easier to remove the magneto plate from the engine.
But this page will show you the location of the points and it's pieces and locations of pieces.
Rough running motor checklist.
If your motor is running, but not right, below is a list of some things to check.
Spark Plug with water on it
This problem occurs when a gasket or head is bad.
Symptoms: motor won't start easily or at all.
If gas is flowing, check for spark.
If no spark is observed, clean and gap points
If gas is not flowing, check for plug/dirt in line, carb, or tank including valve.
If starts, runs rougher than it should, lots of grey/blue smoke that simply doesn't smell right.
This typically occurs if there is a leak on the block or crankcase as seen on this same page.
KEEP IN MIND, if your motor hasn't been disassembled and cleaned all the way inside and out, a certain amount to a large amount of blueish/grey smoke is normal. consider that 'back in the day' 30w oil was mixed with gas very heavily, so a lot of old buildup can created 'burn off' of the old carbon, etc on the pistons and rings.
off smells can usually be caused by water getting past one of the gaskets.
Keep in mind that a rough running motor can often times be a simple tiny piece of dirt in the carb.
I've found that running the motor for a while clears this up in many cases.
If running fine then revving up or quitting, check that the impeller is functioning properly and you are getting proper engine cooling.
also, make sure point gap and spark plug gap are correct.
rough running can be caused by frayed or broken spark plug wires also.
low speed idling should be able to run so slow that the motor is barely firing once a second, acquired by turning the "L" shaped slow speed idle on the engine block to less than 1/2 turn from seated.
a properly cleaned and tuned up engine will idle to a slow trolling speed, the 2.5, 5 and 10's can all idle down and troll nicley.
HD-25 INDEX