+1 for the (powdered) graphite. Does not gum up locks like liquid lubes will. A very little goes a long way - the small tube I have (somewhere...) I bought over 40 years ago.

Thank you all for the tips.  I'll start with thoroughly cleaning the bendix and treating it with graphite.  And try to inspect the flywheel teeth.  The car normally (except this once) starts fine so I'll stick with the oil cooler.  

The most likely cause is, as mentioned, the Bendix needs to be cleaned. It's fairly common on early cars with original starters and starters that have been worked on by someone who don't understand how they work. I usually remove the starter and work brake cleaner through mechanism until I'm sure everything is clean. If it doesn't seem like a lot of work you probably haven't cleaned it enough ??. Graphite is a good lubricant for the Bendix and may help keep it clean in the future. You can use the same stuff you use to lubricate locks.

Kelley

The starter jams because the flywheel is worn out.

If you get stuck in traffic on a hot day you may wish you'd left the oil cooler in there.

Steve,

I had this exact starter and it made contact with my ten row oil cooler.  the original pre-verto starter had more clearance than the high torque one.  I ended up using it anyway and deleting the oil cooler.

Your starter should be fine. It may need the Bendix drive cleaned - no lube!
If I recall correctly, early starters had a square tip on the back end of the shaft to turn the starter motor backwards to release a jam. If it otherwise starts well, I don't think a high torque starter is necessary. If it turned out you had a worn ring gear, a high torque starter may only hasten the demise of the ring gear.

Hi fellas,

I went to start my 1965 mini and when i did i turned the key for a split second, i heard the engine turn over(my fingers slipped on the key). Then as I turned the key again just a click.  I went to check/hotwire it under the hood and found the starter was jammed to the flywheel.  I put it in gear and rocked the car back and forth.  Still stuck.  then loosened the starter nuts and rocked the car and it became unstuck and i was able to drive home.  I've tried starting it bunch of times in the garage since then and it starts every time with no issues. 
My questions-
1. Has anyone seen this before- short start bind up?  
2. Should i just replace the starter?  It looks like the original starter
3.  I like the idea of the High torque new style starter- Part No: C-GEU9404