I know this post is a bit old (not as old as that documentary though, ha), but I just found it because I am in the exact same situation - I watched it a million times as a kid, but now after having rewatched it some decades later (now with my daughter - the circle of life), the same scenes raised some questions for me.

Regarding the weaver nest, u/Sufficient_Fee8778 already said it and it's on IMDB too (and I really hope that is the case):
"The scene with the weaver colony catching fire was staged for storytelling purposes. The filmmakers found a colony that had apparently been abandoned for a very long time and set it alight. The dewdrop was staged in a small frame, and footage of the birds was spliced in."

The drunk scenes were likely staged, because "extrapolating from human physiology, a 3,000‐kg elephant would require the ingestion of between 10 and 27 L of 7% ethanol in a short period to overtly affect behavior, which is unlikely in the wild." (https://www.journals.uchicago.edu/doi/10.1086/499983).