Thank you for properly qualifying your comments with "if that is what the OP has in mind". Actually, in my case, that's not the question. For me, all I wanted to do was take reliable (verbal) "notes" on the phone call, because the unrecorded party refused my request to record the conversation. So, the recording can be used as evidence of MY words during the phone call.
In general, I agree the recording cannot be used to authenticate the unrecorded party's words. But in some case, that might be possible. Namely, if you can get the unrecorded party to agree (in email, say) that the phone call was uncontentious, ahead of time, before the existence of the one-sided recording were known to the unrecorded party (before legal proceedings were initiated, say), and if the one-sided recording were explicit enough (say by always repeating the unrecorded party's words), then the recording does indeed have evidentiary potential.
To Mr. Knowitall:
Well, let's consider that the question has arisen at the Supreme Court multiple times, and those worthies deemed it important enough to address in published reporters. And probably they have a prettiy good insight into the importance of such things.
Furthermore, there actually is a non-trivial question of illegality here. Namely, suppose the unrecorded party's words "leaked" out of the handset slightly, to the extent of being unintentionally recorded as "noise" on the recording, which forensic techiques could recover. Does that then count as an illegal recording of the non-consenting party, or not?
(Incidentally, it would help if you were a little less condescending about things you don't understand.)