And by the end of the series, ER had a completely different cast than the start. One of the issues with Grey's is the title--it kind of has to center around Meredith (I guess it could have switched to a different Grey...). They hang on to many characters way longer than they have a decent plot for them.
As for this episode specifically, as a finale, I think one of the main issues for me is that they were trying to focus on too many plots at once. I feel the best finales of Grey's had them all together dealing with the same issue (like the hospital shooter or the plane crash). Of course, it's over the top to have some major disaster every finale. At the same time, focusing on just a couple plotlines in this one would have made it more effective. It's like you would go from the high-stakes blood donor for the boy to...Maggie and Jackson's camping woes to Teddy giving birth in a fairly straightforward delivery (well, aside from the whole Owen confessing his love--I think if I was in the middle of giving birth, I'd just be like, "shut up until I'm done!"). And Jo getting needed treatment. Oh right, and the whole insurance fraud thing. And Contacts and HAOG. I still feel like I'm forgetting something.
As for Jo going inpatient, she did seem to be having difficulty functioning. Like just laying in bed all day, not really being willing to talk about what happened (except to Meredith), the going to work drunk, saying something suggestive of wanting to die. I think she was a good candidate for voluntary inpatient. Could she have been forced to go legally on a psych hold without seeming more of an immediate threat to herself (or others)? Doubtful. But voluntary, as long as there are beds available--she might be able to get help more quickly than once or twice weekly therapy sessions. Though as someone mentiond, intensive outpatient might have been a better choice, I imagine many viewers wouldn't be familiar with that, so they'd have to do a big explanation. While just showing "Psychiatric Inpatient" on the door was enough.