There is a non compete agreement signed by two parties, it is dated Mar 2, 2010, the agreement reads 3 years from that date. The other party is claiming that the non compete is in effect until Jan. 16, 2014. Can we dispute this?

Usually... but the devil is in the details.

IE... you had a business Say a Pizza shop and you sell it to someone... there is usually a non-compete clause keeping you from opening the same time of business next door (A pizza shop)and taking their clients you had before at your old shop..

THAT would be enforcible... but it you are have a specific job skill and have only worked in one industry... they won't be able to enforce it if you quit to work for a competitor... Like say you quit working for Nextel, and go to work for T-Mobile.

Because I've done it a number of times over the last 30 years. Of course... I didn't take any trade secrets with me... when I did it.

The problem is that my husband opened a business and has been doing the job for the past year. Now the other party is telling him he can no longer keep doing it because of this non compete agreement.
Also there was another non compete agreement signed by another party with my husband that was dated AFTER the original one on Mar 2. that was signed Mar 10 of the same year. Does the second one cancel out the first?

He really needs to hire a lawyer and review these agreements closely... because it sounds like it might end up in court soon. Because the exact wording is going to matter in them.