8-24-11>>> As of today, US silver dimes are worth about $3.00 just for the silver.
It is more than likely a "Magicians coin" which can be picked up for a few bucks. They are usually hollowed out coins, with another coin put inside. If it is a true mint error (extremely doubtful) it's called a "mule" and would be worth a small fortune. If you can snap some good photos, you could post them at http://www.coincommunity.com/forum/ (free) and get some good opinions. Given the fact its 2 different size coins as opposed to a two-headed or tailed coin it is probably hollowed out. You can see how its done here... http://varietynickels.com/articles/twotailed.htm
1964 is the most common date for silver dimes. In circulated condition its value is based only on the silver it contains, about 0.07 troy oz. Precious-metal prices change every day so any specific dollar value posted here would be out of date almost immediately. While it's not normal WikiAnswers policy to say "use the Internet", that's the best approach in this case. You can check a site such as kitco.com, CNNMoney, etc. for the latest spot prices and just multiply by 0.07. A dealer will pay half to 2/3 of that amount.
If the coin is uncirculated its value as of 07/2011 would be in the $4 to $10 range for the most commonly-found grades, but an absolutely top of the line coin (graded MS67) could sell for as much as $80.
1905 through 1920 there were no silver dollars minted in the USA.
They all have a satin finish.