At 04:14- the base of the tree is perhaps 4 feet in diameter but at 04:49- it is much smaller.
When Ward is talking to Simmons to help her scale the tree in the Norwegian forest, Simmons changes position between shots - first facing up the tree, then facing Ward with her right hand across the rope, then facing up the tree again.
Simmons tells Ward she's going to give him 10cc of benzodiazepine to relieve his symptoms. Problem is, there's no such individual drug. Benzodiazepine refers to an entire class of psychoactive drugs (including Valium, Ativan, Klonopin, et al.) commonly prescribed for their sedative/anxiolytic properties. The writers probably were worried about brand trademark infringement, but they could have used a generic version.
At 34:52- The actress rolls into the camera which results in a shaky picture.
On the first section of the Asgard staff found, the runes on the staff spelled out "RAGE", while the second spelled out "POWER", in modern English, just with Norse Futhark runes instead of English letters. At the very least, they should have spelled out the words in Old Norse, if not in the alien Asgardian language.
At 04:23- Jakob knows precisely where the artifact is inside the tree.
At 16:29- just by chance Professor Randolph bumps into a group that is also searching for pieces of the staff.
At 00:48- Fitz could have his drones examining the debris instead of doing it himself "one teeny rock at a time".