My biggest complaints are probably DynamoDB eventual consistency (unavoidable when using GSIs), occasional CloudFormation funkiness (though no urgent prod issues yet, thankfully), CodeDeploy CW alarm rollback jankiness (which doesn't tell you which alarm triggered a rollback!!), and lambda coldstarts. But none of these are too terribly concerning and I have faith they'll get incrementally better over time, hopefully.
The biggest cautionary tip I have is we run all our Lambdas with the max 3GB memory both for peace-of-mind and because the underlying EC2 instances have significantly faster CPU. We were seeing weird timeouts and latency initially with <1GB memory, so I'd be hesitant to run the service if the extra cost of using the biggest possible instances is a concern, which for us it is not.
Another cost concern I should also mention is that we mitigate cold starts by running multiple canaries using scheduled lambdas (in addition to the standard canary role of generating a baseline of metrics and immediately detecting/alarming on end-to-end issues). We are effectively maintaining a constant warm pool which, in theory anyway, greatly decreases the chances customer traffic will hit cold starts. I'm not intimately involved with the financial aspects but I suspect achieving the same effect with EC2 would be significantly cheaper, at least with respect to infrastructure costs. I would guess, though, that the developer time savings achieved by massively reduced ops burden and overall system simplicity are probably comparable to the increased infrastructure cost, and very possibly hugely outweighing it.