My laptop DVD drive has a problem reading some DVDs but not others. It only happens with DVD borrowed from a public library with transparent plastic security label attached to the top surface of the DVD. It never happens to DVD I borrowed from Blockbuster or Netflix and I have borrowed hundreds of them.

Should I be concerned about it? If the problem is with the drive, why does it only happens with the DVD borrowed from the library with security label attached? If the problem is with the disc, why my other laptop can read it? I have cleaned the lens to no avail.

Note: Windows Explorer can't even read the contents of the DVD so the problem isn't with the software player. I have XP SP3, 2.8 GHz Core 2 Duo, 3 GB RAM, Panasonic UJ-120 drive with all latest update installed.
The security label is similar to this http://www.specialtystoreservices.com/productdetails.aspx?productid=17669