@meubanks I heartily agree with you that filling the daily progress bar takes priority, but only after a sim has solved the required number of cases for the next promotion.
If my sim's next promotion requires that one more case be solved, the sim will focus on solving that case first because, as MarianT pointed out, the performance bar fills faster when the sim goes to work alone.
Once the required number of cases for the next promotion is solved, my sim starts a new case assignment and begins working on the next case (visiting crime scene and gathering evidence, if necessary; analyzing evidence). If one is trying to max the career as quickly as possible, doing extra (case-related) work can have its benefits. Like, when my sim arrives at work the day after a promotion, she can issue an APB before noon and solve a case the same day.
My sim is currently Level 9 and has solved the required 6 cases. She only needs to push her performance bar all the way to the right, so she'll only be "sent alone" to the Station from now on.
I'd never done the Detective career before, so I wanted to try it out in my dynasty challenge. For my first three cases, I had problems with the arrested suspects not showing up with me at the station. My third suspect "only" had to be arrested twice and my last two suspects came with me the first time. That was both worrying and annoying.
I agree with you that the Scientist career is the most fun and most useful. Playing the Doctor and Detective careers once each is enough for me, though my sim looks pretty bad when she's dressed in the detective uniform! And I love when she dangles the handcuffs.