Is there any reason I should be leery of a 1950 Ford Club Coupe that has an overdrive transmission? A seller has told me that transmission was plagued with problems. This is the first I have heard of that.
The condition of the individual transmission in the car would be the primary concern. The transmission is very reliable if it isn't worn out or damaged, or has electrical issues. The Borg Warner electric overdrive transmission was used from the '30s into the late '60s/early '70s. If oil is kept in the unit and the electrical circuit is complete it is a very reliable transmission.
The fact that "a seller" is warning you about problems, it is very likely that he has a completely beat-up, screwed with example of something that has proven to be a good unit over the years.
Look for anther, just not that particular one. Or just plan on replacing it; they are out there (I have two).
Is there any reason I should be leery of a 1950 Ford Club Coupe that has an overdrive transmission? A seller has told me that transmission was plagued with problems. This is the first I have heard of that.
It would be nice if the seller would describe the problems. If the problems are with the electrical system that controls the overdrive, those can be addressed with a little work and an understanding of the system. Manuals and parts are available. If the problems are internal, that is a different story.
The most severe problem that can happen with the BW R10 OD is lock up due to failure of the planetary gears. Most problems are due to deterioration of the wiring and electrical components. I suspect that the major failures were due to a hard life with few lubricant service cycles resulting in low oil levels. They are reliable but should be serviced by the factory recommended service schedule.
Back in the early 60s, my Pop had a lock up failure with our 51 Merc but he drove the car many miles to include trips up in the mountains of Colorado with little service. He didn't trust it so he pulled the handle out and unhooked it from the lower dash lip and then wired it up under the dash so nobody could use it. I fixed all that many years later and have very few problems with it. I repair or replace system electrical wiring and components at any sign or deterioration. I use Aeroshell W100 motor oil in it with no plus additive. The Mercury transmission was based on the early ford design which differs from the 259 series used in the shoe box Fords but there isn't a lot of difference. The Mercury cars went to the same 259 series in early 1951 so they are basically the same unit as the earlier shoe box Fords. My two 51s were earlier models that still had the older design from 1949.