general question on purchasing upgrades w/miles
 

When you spend 20,000 (40,000 for international) to upgrade a round trip, is that for all the segments? What I mean is: what if you have one or two connections before your final destination? Are all the segments upgraded or do you pay 10,000 miles per segment?

Not per segment. I recently flew EWR-IAH-SEA-IAH-SEA and used only two certificates (UF0W's) for the upgrades.

Now when I got to the aiport, the ticket agent tried to argue I needed four but after I convinced to call the OPSC she found out she was wrong.

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EWR CO Gold

I found the same thing to be the case. Some gate agents (and even some rewards desk agents) don't understand the rules.
Earlier this year, I was flying from LAX-IAH-CLE-ORD on a full Y ticket (all travel during the same day) and the reward desk person told me it would be 5000 miles per segment.
Needless to say I hung up and called back. I got a more knowledgeable agent who charged me the correct mileage.

I, too, was told that it counts for all segments. I was going to use miles to upgrade from LAX-IAH-CLE and it would have been just 10000. but then the seats weren't available on the IAH-CLE leg and I ended up getting a free upgrade from LAX-IAH.