"Both sides of the aisle" doesn't apply to a 737, since all aisles have windows! Just had to point that out.

I didn't fly the 737 a lot but it was one baby to a row, meaning three seats. We were told one extra O2 mask per cluster of seats (usually).

Airlines can add rules but they can't override FAR's. When we're hired, we have to learn them but we're not always told which ones are specifically FAR's and which ones are the airline's own rules. Irene's example of the electronic devices is a good one. My first company didn't allow blankets over laps for take-off and landing. Guess what happened to me when I changed airline! I'm whipping off the blankets, only to be told by my new coworkers that it's not necessary on my new company.

In case anyone is wondering, no, we are not necessarily told which are which because basically, it's a waste of time. There is so much to learn that we can't spend any time on analyzing it all. No electronics before pushback. Check. No more than one lap baby per row. Check. and so on. Passengers ask for explanations and we usually didn't have time, let alone know all the reasoning behind it all. Most of it is, simple logic though.

It's kind of like the military, to be honest. Remember that the airline person still has to abide by its company rules, even if they're not strictly FAR's.

Ground agents are often from other companies, or here in Europe, there are services that do this, so the GA's are actually employees of an outside company. If they work for multiple companies, they can get the rules mixed up. Also, if they worked for another company, I know from experience that it can be difficult to keep the rules straight.

If you have a special situation, like multiple lap babies, mobility issues, checking special items, etc. scour the airlines' own website first for relevant information. If not, email them so that if a GA says something that's not right, you can whip out that print-out and show them...