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A customer emailed me citing that his bottom bracket is lose and that the fixed cup is on the wrong side.  My first thought was some brute of a previous owner forced the cups in the wrong way, cross threading the bottom bracket and ultimately killed the bike.  I offered to check it out the situation.  When he came it looked like the picture above. The adjustment cup and lock ring were totally threaded out of the bottom bracket from the rotating spindle motion.
Picture 3393
When I saw the bottom bracket though, there was a silver lining.  It read 35xP1 meaning its a French threaded cup.  These bottom bracket setups DON’T have the reverse treaded fixed cups.  This explains problem number one, the cups are on wrong sides because they’re both the same thread, nothing stopped the previous owner from knowing which is which.
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After removing the fixed cup from the non drive side I checked the bottom bracket threads and was glad to see my initial worries were unfounded.  The threads were fine.
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Picture 3413
What you do need to take note of though, is because of the bad design of the threading, the fixed cup needs to be applied very tightly onto the drive side of the bottom bracket or else it will unwind itself out.  One good measure advised by Sheldon Brown is to put thread locker on there.  Clean the bottom bracket shell and cup up real good and give it some Thread locker before screwing it in and hopefully you never have to worry about it again.
Picture 3401 
All done.

Note: French bottom brackets are 35 mm x 1mm 25.4tpi
Italian bottom brackets are the same way with (right) threaded fixed cups but they’re 36mm x 24tpi

Info via Sheldon Brown