Panel 1: Oh jeez. It's like someone said a while back: the strip is snarking on itself. That's ALL he can say, is variations on how obsessed he is with Liz. Meanwhile, for once, Liz has a well-drawn butt.
Panel 2: Jeeeeeeeeeeeeeeeeeeez...
And wow, you dream when you sleep. Well, better than daydreaming about her while you're cleaning your gun, I suppose. And if I didn't know better, I'd think that "Really." had an undertone of "Great; can you change the subject already?".
Panel 3: Liz must not read many romance novels. (Though I'm not sure she reads much at all. Am I correct in recalling that she once said she reads a book a month?) The male lead HAS to have an "unromantic" profession, otherwise there'd be no surprise when he started wooing the female lead. Plus, he has to be established as an alpha.
But forget that for a second. Is he about to reach into his pocket?
Panel 4: Speeding? No, my dear, he went offroad weeks ago.
Panel 5: Blaugh.
ETA: And on further reflection, the only difference between this and Howard's approach is that a) Paul is not insulting Liz ("Lawrence lets YOU drive the forklift?!") b) he's conventionally good-looking and c) he's Elly-approved. And being a cop affords him more opportunities to breach her privacy...