When buying an older home that has recently been renovated, what should I look for in the home inspection?
Check with the local building department to verify that they pulled permits and passed inspection for the work.  They could have just covered up big problems that inspectors would have forced them to fix.

Even if they did get permits that does not guarantee that there are not still problems.  Things that may have been hidden from the inspectors, just missed by the inspector, or some issues may just predate the "flip".  You definitely will want an experienced home inspector to check everything thoroughly.