Can I Legally Record a Conversation Between Me and Someone Else

It really depends. I'm not being obtuse - truly, I'm not.

But you're being so very vague - there could well be circumstances in which there is an expectation of privacy even if you've consented to the phone call being recorded.

Can you give us details?

well between me and my sons mother there is a lot of fighting because we have split custody. we have a parental agreement which is just as vague as I am being here on this chat forum, however there are two specific things we did agree on and sign for which she blatantly dishonors on a weekly basis: one is the facilitating of phone contact between my son and myself while he is at her house, the other is regarding the specific times which she is supposed to be available for transitions between households. There are many phone conversations during which she both acknowleges and blatantly dishonors the custody agreement as well as other agreements we have made since because she would rather; go to a party; go to the mall with her girlfriends; help friends move ( one friend she helped "move" for almost two months) instead of take her son on the days she agreed to in the custody agreement. aside from these things which I have mentioned, there are other things which com up in our phone conversations which I wish to god a judge in a court of law could hear - their jaw would drop. I basically want to prepare myself with evidence of her abuse of our agreement, as well as the law if and when the time comes.

I really would like to record and use the recordings to show a judge or other authority of the goings on with regard to her behavior. my question is can I do this?

Yes, but I'll give you a heads up here.

Don't plan on the court being impressed with several months' worth of recordings. If there's something amiss, you need to act upon it AT THAT TIME. It comes across as sneaky and vindictive when one parent "saves" evidence to present all at once - if the parent was genuinely concerned, s/he would do the right thing.

It also depends on what EXACTLY your custody order says....is Mom actually in contempt here?