Does a mistake make my artist print more valuable, or less so?

Be weary of limited editions. Learn about them before you think about buying. Some may be forgeries or the signature can be part of the printing process.
Here's a good primer: http://www.artbusiness.com/certaut.html

This came directly from the artist's own gallery, and I walked in there myself and ordered it, so I'm not concerned about that. The artist signed the print, and wrote the incorrect number on it, and they have offered to replace it, saying they will destroy the one with the error on it. I need to find out if that's wise, or if I would be smarter to keep the one with the error.

Actually, it's better not to worry about "value," but how much you enjoy the artwork. We have original and limited edition artworks in our home, because I like the artwork. I bought one large original oil painting in New Zealand that's in the living room that I really enjoy - every time I see it. The scene is three men sitting around a box with a tent in the background, and one man on the right side playing a harmonica. Another original oil painting was a gift from Dan Piel. He worked as a director of an ad agency in NYC, and ended up teaching graphics and art at Cal Poly in California. I met him on an African safari, and he gifted me with a painting upon our return. It hungs in the entryway of our home. One art work I bought in Shanghai, China, at the art and craft store is a poster of a Japanese woman with a fan. It looks like an early 20th century work.

Why don't you ask the artist?
I'm a long time artist, not particularly famous, but I've been partner in couple of galleries in my life. I'll suggest you listen to the artist.

I'll give it a shot.

The reason I didn't go there is that the gallery owner only presented me with the option of returning it or exchanging it. He didn't address the possibility of my keeping it. He said if I return it, they will destroy it. I don't know what to make of that. I get that they would need to destroy it, because then they would have 101 prints out there instead of 100, but my keeping it would certainly be the least expensive option for them, and involve no hassle. I'd think if there were a benefit to me to keeping the print (i.e., that it has more value), they would suggest that, because they are going to literally travel 5+ hours to pick this one up from me.

I will either keep this one, or exchange it for another, because I do enjoy it and that's why I wanted it in the first place. So it's not about enjoyment. I just have had so many problems with this thing that it's made me not ever want to do business with this gallery again. The thought that they could be literally trying to screw me on top of everything else (by taking back a potentially more-valuable piece of artwork and replacing it with one less valuable) irritates the crap out of me. If keeping the print with the error is to my benefit, I want to take it because of all the hassle.

However, if the print is LESS valuable because of the error, I definitely want them to drive the 5 hours out here and get me a new one.

My point is that they have messed up this transaction in every possible way and turned something special for me into something that has made me angry. I want the best possible outcome for me from this mess.

This is the key to owning any art work. Many decades ago while my wife and I were visiting San Francisco near Girradelli Square, we walked into art store, and bought an original oil painting by Sumner. We paid $300 for it. Many decades later, it was worth $3,000, but it doesn't matter, because we're going to keep it.
His style changed considerably since we bought his painting.

I understand that. I'll have the print either way. I'm just trying to figure out if my current incorrectly numbered "50/200" in the artist's own handwriting is more or less valuable than one correctly numbered as "50/100."

https://fineart.ha.com/worth/art-value.s?type=google_%2Bvalue%20%2Bart_nid-g-cid-211286686315-mt-b-device-m-ap-1o3-dm--clksrc-kw-cmpnid-743212699-adgpid-37679781246-fditm--locphys-9032152&gclid=EAIaIQobChMIkJrvt76t1gIVlYJpCh1VjAmqEAMYAyAAEgKBA_D_BwE