OK, from your second post, looks like two issues: hesitation and flooding. Taking them in the order I would consider the most important.
The flooding can be caused by:
(1) defective or dirty fuel valve
(2) defective or incorrectly set float
(3) cracked housing where the fuel enters the carb (very unlikely)
(4) excessive fuel pressure (have you installed an electric pump?).
(5) blocked or missing fuel tank vent (can creat too much pressure if too close to the exhaust)
Always install a new fuel filter after the carb has been rebuilt to protect the work done.
Hesitation:
Yes, hesitation can be caused by a defective accelerator pump in the carburetor, but highly unlikely in a Zenith with a fresh rebuild.
Much more likely to be in the distributor. If that model has a vacuum advance, is it working? If not are the distributor plates free (not sticking) and thus allowing distributor advance?
Now as to the linkage being loose:
Play in the throttle shaft IN THE DIRECTION OF THE SHAFT IS NORMAL.
There should be some play (or clearance) between the shaft and the throttle body. If there were none (or too little clearance), then the shaft would bind in the throttle body when the engine was hot, due to the coefficient of linear expansion.
The design tolerance of shaft to body (the direction perpendicular to the shaft) when new was 0.004~0.006 inch. Wear in the field as much as an additional 0.003 (so a total of 0.009) inch is acceptable. This is easy to measure with a dial indicator.
More than 0.009 can cause idle issues; but may be repaired either by installing throttle bushings or a new throttle shaft or both depending on the location of the wear.
Jon.
