I think anything big, like design, portrait, country name, or "Silver Certificate" would be noticed very quickly.
I might notice some small changes, but most people won't. "When was Paul Krugman Secretary of the Treasury?" I once collected coins, and I still check coins and bills I get, especially old-looking ones.
Probably the least likely thing to notice would be a coin or bill from the future, if it was otherwise identical to the current coin or bill. "A 2015 penny?"
Even funnier, an ordinary-looking 2010 (or 2009) penny.

(IOTL, in 2010, they changed the design (and in 2009, ran a line of commemoratives). One would actually expect a 2010 penny to look mostly just like a 2008 one - but IOTL it doesn't.

)
In a similar vein, a non-state quarter from 1999 or later (even 2015).
In fact, a 2015
penny would be rather likely to be noticed, more so than just about everything else (up to, and maybe even including, say, a Clinton (or even McCain) presidential dollar).
The reason? Well, the Lincoln bicentennial should have happened ITTL as well as IOTL, and 50 years is a rather long time for a single design, really. So it would still be reasonable to change the design (even if without the commemoratives); if the POD is early enough, the design will probably be different, making the coin stand out - but even the OTL design, uncommon as it is so far, would be something to be noticed, after what looking for the date is almost a certainty.
Heck, I look at all coins I receive, and pick out everything I think outstanding... like an uncirculated-looking coin from 2007. Anything ATL would be immediately noted as such, unless it happens to look exactly the same as OTL, which BTW isn't as improbable as it sounds - but with roubles requires a rather late POD. (Well, either that, or really badly degraded so I can't tell the difference; but then, I wouldn't take such a coin anyway.)
...So what, how?

January First-of-May