The Treaty of Hidalgo set up installment payments for the $15 million
indemnity to Mexico of $3 million a year. Which a review of the
State of the Unions from 1848 - 1852 seem to show those payments being
made. Yet at the Mexico History Museum in Chapultepec in
Mexico City the exhibit on the North America Invasion states Mexico's
land was taken without payment. There also seems to be some that
believe payments were made but not the full $15 million amount. Can
someone reconcile these opposing views?

This is just a free comment and NOT and "answer" to your question,
which only an official G-A Researcher can post  - one with a blue
name.

I have looked at quite a few sites about the treaty, and found nothing
that suggested that the USA did not complete the annual payments.

There have been other breaches of the treaty, as this site mentions:
http://www.geocities.com/rubyhatchet/guadalupe_hidalgo.html

It would seem that among the criticism of the government such a basic
point would have been mentioned, also on other sites.
Incidentally, the problem mentioned on that site, as the subject of a
GAO paper in 2001:
http://www.gao.gov/new.items/d01330.pdf

However, this site gives some further insight on the subject of the
payments, interpreting the Gadsden Purchase in 1853 to be a
renegotiation and reduction in amount of the previous treaty's
agreement:
http://www.progress.org/gads.htm

If this is a correct interpretation, I suppose one could say that
fulfilment of the Gadsden Treaty settled the matter, leaving it a mute
point about what happened between 1848 and 1853.

As to the Mexican museum's interpretation:  It certainly would not be
the first time that the way history is presented in countries that
once were at war does not agree.  In the Mexican War, the territory
was taken before any treaty was drawn up, and the USA probably could
have continued to defend the area without a treaty or payment.

But the USA wouldn't something like that  - good neighbors and all.

I hope someone can find something more definitive for you.

I wrote to the museum with your concerns/question...I will post their
answer if received.