I was thinking a lot about Continuum the other day, and I remembered this mistake I made during that campaign. The inverse/solution to that mistake should have made it to the "Making History Real" section of my Continuum GMing tips.
Basically, when choosing which elements to use to "sell" the past, it's really important you not choose elements your players know better than you do. On a related note, it's important to know when you're being subtle, and when you're not.
Should someone catch you in a mistake in an area they do know, it's not for me to say whether it's better for you to bluff or just own up to it. A successful bluff means more verisimilitude, but a failed bluff means you've lost their respect. Probably, honesty is the best policy... but it depends a lot on your play group. If you're gaming with the sort of folks who will start challenging you once you a mistake - well, bluff this time, and start looking for a better group to game with next week. In my case, I was lucky enough to have a really good group, and screwing up one very minor detail (and stupidly lying to cover it up) didn't have any major ramifications down the road - just a momentary panic and embarrassment, which I now dredge up as an object lesson.
I'd tried, foolishly, to switch up my background music as we moved through the eras. I made no mention of it in-character, I just quietly double-clicked on a new playlist the first time the party went back a few hundred years. I thought it was cute, almost clever. I wanted this to be barely noticed, just a way I could subtly shift the mood of the game as they time-traveled in an earlier era. However, it was apparently jarring. Not surprising, in retrospect - one moment the background music was Classic Rock, the next it was Classical. Of course they'd notice.
Mid-scene, about two quarter-notes in to the music switch, one of my players drops character, looks me in the eyes, and asks: "You do realize this song wasn't composed until roughly 170 years after the era we just spanned to?"