In the movies of the Mambo and
Salsa basic steps on Ballroomdancers.com, it looks to me as
if the dancers are beginning the steps with their body weights opposite to what I have been taught. For example,
just before the man steps with his left leg, his weight appears to be on his left side, whereas I was taught that just before one steps with the left leg, the weight should be on the right side. My 2 questions are: am I viewing the movies correctly and, if so, was I taught correctly? Thank you in advance for a reply.

Here we go again--

It depends largely on where you get your info.
Initially (back in the 40s-50s and still today in chain schools ) the man was taught to commence side left-- break back on 2-- this is named the " call and response " theory ( some say fwd on "2" is more correct ) and follows the clave rhythm, which is more accented on "2" of the 2nd bar in the 2 bar sequence( on 6) .

Commencing fwd is also very common ( on 1,2 and or 3 )the reasons given all have some validity .
If you are really interested in indepth origins, there are numerous sites that will supply all that info.( Salsa Forums ) ( I could do this, but it takes an hr to type )

Bottom line-- choose what makes you comfortable-- and try the different styles