So this is why our API had a rash of 500 errors last night. We haven't been very happy with the uptime of this service, mostly because they do deploys that break things for a couple minutes about once a month.
Do you use Lambda as a backend? If so, this might have been related to Lambda, not the API Gateway. I also saw a number of 500s, but upon further digging, the API Gateway was fine, but the Lambda functions it was invoking were returning "Service Error." Still not happy either way, but I've generally been impressed with the gateway product itself.
Everyone acts like being locked into a provider is the worst thing that could happen. When it comes to monitoring, if I'm using other AWS products, I don't mind being locked into AWS monitoring as well. Because I'm either going to just use it and be done with it, or I'm going to spend months and lots more money finding a non-AWS solution that integrates as well with AWS. If we ever switch away from AWS, I'll invest the time then to use a new product, but until then, we accept the trade-off for saving lots of time and money.