Backdoors in open-source software where discovered, yes.
Generally speaking open-source does not automatically mean the software is secure or free of bugs. Just remember Heartbleed in OpenSSL.
One of the main problems is that everyone could take a look on the source but often no one actually does thinking someone else surely did it before. So it is possible that there are bugs or backdoors for a very long time hidden in some project.
Another Problem may be the complexity of some projects, it is just not possible for a single person to look at the source and know it is safe or not - you would need a long time to accomplish this just see the security audit of TrueCrypt for example.
In this context a main problem of open-source is that everyone can modify the code and share his own programm. There are many cases of this, manipulated versions of big open-source programms like Firefox, PhpMyAdmin etc. The normal PC-user won't ever notice that there is something wrong but he is happily using a big backdoor.
So open source may be a little bit more secure because in theory everyone could check the code but in practice bugs or backdoors may be undiscovered for a long time. And please don't get me wrong, I'm a big fan of open-source software but I am aware of the risks and so should anybody else.