Another thing to consider is that back then there were only a limited number of games that were even filmed. So most likely the old games that you've seen were marquee matchups and thus more likely to have higher attendance.

I'm no expert by any means, but I liked your question. Here is the attendance numbers through the 1930s:

http://www.ballparksofbaseball.com/1930-39attendance.htm

You can see that very few times did a team break 1 million visitors for the year. Stadiums were much smaller back then, but even for a 20,000 seat stadium for 77 home dates (they only played 154 games back then), 100% capacity would be over 1.5 million people.
So for most teams they were only half filled. I know my numbers are crude, but capacity for stadiums fluctuated over the years. I used 20,000 as a conservative number.

I suspect that when you see packed stadiums in movies, it's to highlight the popularity of baseball back then. Here is a nice piece I stumbled across for baseball in the 30s:

https://historyrat.wordpress.com/2010/01/02/the-golden-age-of-baseball-the-1930s/

The answer is no - for the most part, baseball teams did not sell out games.

A look at 1927 on baseball-reference shows that the vaunted 27 New York Yankees had an attendance of 1.1 million in a 154 game season (77 games at home).

Yankee Stadium I in 1927 had a capacity of 62,000 for a capacity of 4.7 million over a 77 game home schedule - meaning the average capacity was closer to 1/4 for one of the greatest teams in baseball history in the most populous city in the US at the time