LOL, I finally got my sister to watch Nancy Grace with me one night over the holidays when they were replaying the interview tapes and at the exact spot you've mentioned, my sister (who knows almost nothing about this case) was like "WAIT?!? I thought she didn't have a job? How was she coming back from work??? I don't want to listen to this anymore, she freaks me out."
I think it's part of Casey's MO that, in order to communicate with her, you HAVE to be willing to engage or sidestep several lies to make any sort of headway. And it's important to remember, IMO, that at this point, LE thought they were working against the clock to find and save a living child who was in danger. If they had stopped Casey at the "on my way home from work" lie, they wouldn't have gotten to address the most important issue: where she supposedly left Caylee.
I think a lot of the jaggedness and conversational cut-offs occur during Casey's interrogation because LE knows time is of the essence. Casey clearly doesn't care about this and so they have to direct and redirect conversation away from her pesky phone charger and everything else she blathers on about, so they can obtain the necessary info and find Caylee.
I think the time-sensitive imperative to find a missing child also accounts for LE's decision to arrest Casey so quickly-- another thing LE is now being criticized for. I do think the decisions and tactics used by LE at this state of the investigation reflect that their sole purpose was to recover a missing child. Retrospectively, those choices weren't the best way to ensure Casey's conviction, but I think LE had their priorities straight from Day 31.