If it is now running well under load and you are just a bit dissatisfied with the idle, there are some simple procedures you can go through that might improve it. Before doing this though, are you sure that you adjusted the idle mixture, and assessed the idle quality, with the air cleaner fitted, and the choke wide open? Have you set the idle speed for 1,750 rpm? Did you bear in mind that side valve engines normally miss some shots at idle, but should nevertheless run steadily at constant speed? (The idle quality needs to be compared with other single cylinder side valve engines, not with OHV, OHC, or multi-cylinder engines.)
First, check that the carburetor is not flooding. Turn on the fuel but do not start the engine, and see if, after five minutes, fuel is dripping from the top of the float bowl, or coming out of the jet in the venturi. If it is flooding, mixture will gradually become overly rich at idle and tuning the idle jet accurately will be impossible until you fix the problem by servicing the needle and seat.
Second, check the idle mixture screw setting you ended up with after adjustment. To do this, turn the screw gently clockwise until it bottoms very lightly, counting the turns and the final fraction of a turn. It should have been open approximately one and a half turns. If it was very far away from this, go through the idle mixture adjustment process again. If you consistently find it needs to be open substantially more than one and a half turns, you will need to clean the carburetor, paying particular attention to the idle system.
Third, bear in mind that you did not tune the engine, it is as received except for having adjusted the mixture. Whenever you acquire a second-hand engine in unknown condition, you should clean or replace the air cleaner element, clean the cooling fins, ensure that the choke is opening and closing fully and correctly, clean the spark plug properly and gap it (or replace it), check the tappet clearances, and test the compression. After doing that, and mowing the lawn so that it settles into its improved state of tune, adjust the idle mixture again using the same procedure as before. If the idle quality is still poor, we will need to discuss it further.
