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Wait wait. What would happen if a long half-strand of DNA tried to pair with another but there was one letter wrong in the middle?
Something called a "lesion" around a base mismatch, basically a bubble in the strand pairing. It can introduce kinks in the helix, and generally is the result of mutation in one strand.
If that's how DNA worked, I imagine it just wouldn't pair, but that's not how DNA works. However there can be and are many mistakes in the transcription and translation of genes, they're called mutations and they're the mechanical cause of cancer. The kind of spontaneous mutation your imagining is unlikely to lead to cancer without other contributing factors, and the body has numerous control and correction mecahnisms, but there are billions of base pairs (i.e. A—T is one base pair) in each cell of the body getting transcribed and translated over and over and over, so quite a few mistakes get through.
Alas, it could never be