I must have gotten confused with the bike upside down while installing it.
It was so tight installing it, I don't think it will come loose.
I have about 75 miles on it so far.
Is it a big deal to leave it?

What do you mean backwards? The left cup is in the right side and vice versa? If that's the case, the frame material may decide the fate of your bike.

Wow, I'm not sure I could do that if I tried.

Cartridge French and Italian , being RH thread both sides it.s possible, if its loose ball you could have just fit the axle in backwards
putting the rh thread end in the LH threaded frame ... wow thats gotta be worthy of a Darwin award ..

Well the threads in the bottom bracket have been fubared since day one. English thread BB, yes left cup on right, right cup on left. Funny thing is I just removed it, and re-installed it properly and it threaded in perfectly with no excessive force. As for the darwin comment..uhh.ever heard of dyslexia?
I should have taken a picture to who it installed in both manners.

If it holds, you're golden. If not, a threadless cartridge may be in your future.

I'm confused...maybe it will be more clear if I type it out.

Right side BB is reverse thread...left side of frame is not. Left side BB is standard thread, right side of frame is reverse thread. How can you even start either side threading?

Nope...not more clear now that I've typed it out.

Glad it worked out for you though.

I'm not actually that surprised. I've found that some frames are a very sloppy fit on the threads to where the fit is so wobbly I'm surprised that they don't strip.

Compare the loose fit of many BB shells to the the thread fit on a camera filter lens. It's like night and day for quality.

Front wheel drive?

There are repair bottom brackets which don't use the threads. I am sure you could find one if you did a search.

The best thing to do is to take it out or have a shop do it. it was not designed to be in the opposite way.

About mounting backward.. for left/right thread is plain stupid, but is achievable if the threads are already mashed.

I installed the spindle backward on purpose to adjust the chainline (i swapped double rings with single ring for fixed gear).

Also on italian/french (same thread on left/right), the cups have different lengths from the face to the raceway of the bearing, so that gives more options to adjust chainline by installing the cups backward, or the spindle backward or both.