1973 Evinrude dies out when in slow throttle or shift....

Like the subject says my evinrude dies out when i move the tiller from start spot to the shift or slow. Whenever I move it up to far it dies out. When I slowly move it to shift the rpms drop enough to allow me to shift just fine and it runs great at the fast setting. What could cause this and will it do harm to my engine?

Sounds like your low speed needle/jet in your carb is clogged or dirty. Might try to run some seafoam through her for a tank ot two, but you'll most likely need to clean and rebuild the carb.

I thought of that but was confused as to why it will idle all day long. I will definitely check that out. Thanks.

Before you go into the carburetor as has already been suggested I would check to see if there is an idle stop screw that can be adjusted. Normally that screw is located at the junction of the throttle gears visible on the port side of the engine. This screw can be used to set your low idle stop.
Second, you should have an idle mixture screw on that engine. When the engine has been warmed and is at the proper static waterline (boat in the water) turn the screw in increments of 1/8 - 1/4, turn clockwise and wait around 30 seconds after making an adjustment to evaluate the change. If the engine is/was too rich the engine will speed up, run smoother, and eventually spit lean or "sneeze" and probably quit. Back your adjustment back out between 1/4 - 1/2 turn from that point and leave it there. Your idle stop will need to be reset once you make a proper adjustment. Your mention of the fact that the engine will idle all day long indicates you probably have an internally clean carburetor.

Thanks for the response Pappy! I will give that a go when I have some free time! The PO said that the carbs were cleaned and rebuilt before and I have never seen an engine with a dirty carb run so smooth. It idles fine and speeds up without hesitation. I know my jet ski acted up big time before the carb rebuild. The guy I bought the boat from may have had no idea what he was doing with the idle settings. I will report back with any news!