So this has happened to me several times now, and has required a reload to correct it. Unfortunately in the most recent case I've simply played too many hours beyond dismissing Nick Valentine to warrant going back...
Frequently I am finding that when I dismiss followers in favour of another they are disappearing from the game world entirely. I can go to the location I sent them, wait for an entire in-game calendar month, but they will never show.
It first happened with Piper early into my game, to replace her with Nick, and having sent her to Sanctuary Hills she never arrived. After 2 in-game months of Waiting at Sanctuary Hills I gave up and reloaded the earliest save I could find with her still in the game.
Same happened with Nick after replacing him with Cait. I picked her up from Oberland Station (where I had left her) and sent Nick to Oberland Station. Made sense to me. One straight swap for another. When I came back Nick wasn't there. I rang the Bell (I've added one of those to all my settlements), but he didn't show. I checked all of my settlements, to see whether I'd mistakenly sent him elsewhere. But no. Nowhere to be seen.
I checked his offices in Diamond City, and the Dugout Pub, but no. Nowhere to be found. I went back to Oberland station. Still not there. So I abandoned 3 hours of game progress to revert to an earlier save, before he disappeared.
Two night back I had Nick offer me his personal quest, the Eddie Winter Tapes. I was in the middle of Curie's personal quest (where you have to wait for a day) so was doing other minor quests with Nick to pass the time. I dismissed Nick to head back to the Memory Den and collect Curie. I told him to go to Tenpines Bluff. So I thought. And went off doing other things (such as a buttload of settlement building) for a good 4-5 hours. The following day I clocked up similar, liberated a beach and a Mansion. Set those settlements up.
At which point I thought I'd go back and collect Nick, and start hunting down those tapes.
Only Nick was not at Tenpines Bluff. I rang the bell. No sign of him.
Here we go again, I thought...
I went around all the settlements, ringing bells, and not finding Nick.
I waited a month in-game and repeated the process.
Still no Nick.
Checked his offices. Check the Dugout. Nothing.
I'm really reluctant to abandon such a large chunk of in-game progress to revert to an earlier save where I know for sure he still exists in. Which puts me in a bind.
I completed Reunions long ago. I've done his case file missions. The only other Quest circumstance I can think of which will place a quest marker on his his head is to find all 10 Eddie Winter Tapes. At which point I'll need to return to Nick in order to continue that mission.
But at that point I'll not have had Nick around to respond to having found any of the tapes. Kinda defeats the point.
There is clearly some kind of flaw in the Dismiss system. Some kind of bug which is occasionally losing track of followers. They may not even be out of the game, just wandered off somewhere unplanned. On PC of course you can just force them to spawn in front of you with the command console.
On Consoles this is not an option...
This is a problem that used to occur in Skyrim also, so I imagine it might just be an occasion flaw in the game engine. I would really love it if Bethesda made some kind of tool allowing you highlight where on the map each follower you have collected currently resides. It would make this procress so much easier.