You can Google for silent truncation for a quick example. To be fair, MySql > 5.6 has fixed some of these issues and it also has some flags that can be set to help prevent them.
The by design part is referring to early versions of mysql and discussions around it purposely did not care about ACID. Speed was the number one driver.
I was recently advised by a DB consultant whose area of expertise is MySQL that 5.7 is still too new and risky and that he would advise against upgrading for at least another 6 months or more. He feels that the releases come out much, much too unstable and unpolished and that it typically takes at least a year since release before he's comfortable running it in production. I don't know enough about MySQL to know if that's true or not.
We are now investigating switching to MariaDB instead. (I'd personally love to move to Postgres, but that's not likely to happen any time soon)
I can confirm that the query optimizer introduced a rather serious bug (significantly suboptimal plan for queries involving low cardinality indices), which caused serious issues in our system.
This, in addition to the fact that index merging has been broken in MySQL 5.6 for more than an year now (in some cases it will cause empty resultsets to be returned), and that it is still broken on MySQL 5.7
Beware slight ddl incompatibilities. For example Maria will dump timestamp field size, which mysql doesn't understand (or was it the other way around?...)
The by design part is referring to early versions of mysql and discussions around it purposely did not care about ACID. Speed was the number one driver.