Yes MySQL does buckle under load, and it will break eventually.
MySQL is very fast with low concurreny and simple queries.
If as you get more concurreny queries, or the queries get more complex, mysql slows to a crawl, and worse; it can die.
PostgreSQL, Oracle and MS-SQL are not as fast with low-concurrencty, and they will slow down too, but they will keep going.
But by far the biggest 'bad thing'(tm) about MySQL is it's complete lack of functionality.
In their race for speed, the mysql dudes took out everything that makes a database usefull, like consistency checks, PK/FK relationships.
That lack of functionality does make what's left very fast, but it also means you have to to 5 times as many queries to get to where you want to be. So where's the advantage?
:-)
Don't get me wrong, I really hate MySQL. It's severely overrated.
Getting better, but still no where near 'an option'.