I had a couple RP scenes over this past game that COMPLETELY got away from me. What I'd budgeted for roughly 1.5 hours of my session turned into a nearly 4 hour grind w/my players all over the town and wanting to chat w/each individual NPC.
Should I have run everyone in "rounds" like combat or something?
With something like that, I'd say just go around the table. initiative is generally only used when timing is important, like combat, or someone saying 'I pull the level' when someone else wants to stop him.
If you want a rough idea of how long it takes the PCs to track down the NPCs and have these conversations, Gathering Information takes 1d4 hours. Those who roll 4s will get fewer chats in a day than those who roll 1s.
Imo, it's easier to follow a conversation if you do one person at a time: First, Joe the Fighter gets to ask his questions of Fred the Bartender; then we move around the table to The Amazing Wizzo talking shop with the local arcanist Mumford the Magician, or whatever.
Is your problem that some of the players are getting bored while the others are in the spotlight? If so, you might want to do purely RP gathering information conversations by e-mail or phone or something between sessions and let them compare notes next time they all sit down at the table together.
I think what threw me was that I had planned, based on input pre-game (over email) for a limited amount of stuff. Once the PCs got back to town they wanted to do more than I anticipated. On top of that some of the players who really enjoy roleplaying really wanted to chat out some of the scenes I was going to handwave.
During this interplay I feel like I sort of lost order at the table. As a result the RP went long, one player sort of got left out of their part in it all and I feel like I let my whole table down. I did get some feedback from one player that they felt it was a good session, so I suppose it wasn't a total SNAFU.
It just occurred to me, after we wrapped, that maybe had I just reined everyone in and taken individual turns or used an initiative system or something, I could've steered to the really important stuff and gotten the next adventure started as I'd planned. Maybe I'm just overthinking it though. I asked all of my players for feedback; 2 haven't said anything yet but one as I said had some concerns but overall had fun. Am I just a nervous Nellie?
If your players are having a good time, there's nothing wrong with a session that's largely (or completely) RP. Just think of it as you being prepared that much further ahead for the next session.
If the players are beating a dead horse because there's just nothing more to learn in a particular area and they're convinced there's more clues hidden if they just dig deep enough, don't be afraid to drop character and say, "Hey, guys, you've learned all you can learn here. I'm not going to screw you over with Ha ha, if only you'd been more persistent with the NPCs in Whoville, you would have learned the key to the villain's downfall. This is just it for these NPCs in this location. They've told you all they can that will help you. Let's move on."
My group doesn't really use initative in RP situations. For us, RP is one of the joys of playing this sort of game, and putting an initative counter in those sorts of sessions just makes it that much harder to engage in RP and enjoy the playacting. I don't think we've really ever had a problem with someone feeling "left out" or "missing their turn" or what not, because we're all familiar with each other and just jump in whenever we think our characters would have something to say - basically, as much like real conversations as we can make them.
No, never use initiative outside of combat. Ever.
Non-combat scenes should just flow naturally, in a way that feels right for the party. Knowing the group and what they expect, as well as having a good understanding of story structure and pacing is critical to that venture. If you lack those skills, don't worry, you can learn, and I suggest you start trying to develop them, as they are quite important to good GMing.
Just jump around--make sure nobody is doing nothing for too long, but don't cut into any scene's momentum for the sake of arbitrary fairness. Most players will be happy to give someone else extra spotlight time if the scene is compelling enough, and will be happy to get the extra time themselves, should they require it.