In Active Directory, what is the relation between IP, MAC, and OS?

I have one machine on which I want to run 2 different OSs, dual boot between Windows Server 2008R2 and 2012R2 (or others). I want to keep the same computer name, the same IP address, and the same MAC address.
Will I encounter any kind of issues with the AD and DNS when switching between the 2 OSs?

Do not do this. Two different installations of Windows can not share one name in Active Directory. They must have different names, else the latest installation (relative to joining AD) will overwrite previous ones.

Sharing an IP is fine, and may be default depending on your DHCP server (it's somewhat common to offer the same IP if the request comes from the same MAC each time). DNS doesn't care left or right.

Chris is right. To expand on his answer a bit, the computer's "name" is something that is rarely used by AD. It is simply a human-readable representation of the object. For most operations, AD uses the Security Identifier (SID), which is a GUID comprised of components that represent the domain and the relative identifier of the object.

When you join a computer to a domain that has the same name as a computer that is already joined to the same domain, what actually happens is that object is deleted and re-created with a new SID. This effectively makes the computer that was previously joined "untrusted" as AD no longer has a record of this SID. Essentially, if you have two OS installs (computer objects in AD) with the same name, only the most recently joined one will function properly - as Chris has pointed out.

Agree with Chris S. When you build a machine, and join the domain, the machine's SID is recorder in Active Directory. If you attempt to run multiple images with the same name, but different SIDs the "trust" between your machine and the domain will be invalid as and when you switch between images. In short, you'll end up having to drop-out-of and re-join the domain each time you switch between images. You therefore may as well either maintain separate computer accounts.