This was funny. Especially since I've been to the marriage license office in Las Vegas, where a relative of mine got married (an actual Elvis wedding on the Strip). The applications are found in the lobby at a kiosk. You actually fill out the application in pencil, then stand in a roped line on the right just outside security. Then you wait to be called into a separate room off the lobby with a bunch of counters, kind of like a bank or fast food line where the person at the counter yells, "Next!" I didn't get to go in there, myself, because only the applying bride and groom are allowed inside.
In the wedding I attended, Elvis sang a few songs and then performed the ceremony (the Love Me Tender package at the Viva Las Vegas Chapel). Then the bride and groom went off to the side to have an actual judge or Justice of the Peace do the legal ceremony, and then sign a few papers. It was fun.
I loved the scene with the bored marriage license lady who decides to hit on Clark. And then the Tank reference.
The only "problem" I could find is that the marriage license office is always busy with a pretty long line and a lot more than a single employee manning the counter(s). There's no front desk where an employee hands you an application since the applications and the pencils are at a kiosk and the instructions are on a sign. But hey, who cares? It's funnier the way it's written. I love it!
P.S. For those who are curious, the chapel next to where you get the certificates is called "A Little Chapel by the Courthouse."