During my searches, I see tons of topics on .NET 4 / .NET 4.5 compatibility. I am taking over the development for multiple projects which were started back in 2004/2005 and are using .NET 2 - .NET 3 & 3.5.
I have the option to use .NET 4.5 - but I want to be sure it's safe to begin using in production systems.
Yes it is.
It was released in 15-August-2012. More than enough to have it tested by early adopters.
Depending on your project, the best thing that you can do is changing the .NET version, deploy it to a new server and run all your automated and manual tests against it.