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Yes! Absolutely. You should check for SILVER coins, which are 1964 or before dimes, quarters, half dollars. To make things easier, look at the edge of the these coins. On the edge of current coins, you will see a line that is copper in color because the current coins are like a sandwich with silver - copper - silver in color. The 1964(and before) coins do not have the copper line because they are completely silver, no copper, no sandwich.
As for old dollar bills, I have to say no. Old bills don't have a lot of added value. Some bills are 'star notes' which means the last character is a star, not a number. These bills are replacements for bills that were damaged or returned to the mint for one reason or another. The star notes are interesting, but also they do not have a lot of added value.
Finally, the TWO dollar bill. Some people have posted videos of going to a cashier and presenting a TWO dollar bill. The joke is on the cashier because the cashier often says 'this isn't real', but it is real. Just not very common. If you get a TWO dollar bill, it is always an interesting item to have. You can get a TWO dollar bill at the bank. It has no added value, but it is interesting. As a cashier, don't say the TWO dollar bill isn't real. If you want to have fun, give a TWO dollar bill to someone as change and watch their confusion as they say, 'this isn't real'...

This is extremely interesting! I'll be looking out for these from now forward!

I know pre 1982 pennies are made with more copper, and are worth more, but they're also illegal to melt down to get the copper. Do you have an opinion on collecting these for future value, or would something like this be a waste of time?

The Old Man from Pawn Stars is collecting pennies. There was an episode that mentioned his barrels of pennies and the youngest guy was saying it was a waste. The Old Man was adamant that it is worth saving. . .
I think is is worth saving, but it ends up being VERY HEAVY and BULKY. So I have not started saving in barrels like the Old Man.

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