When the ambulance brings in Hank, the EMTs tell the staff that the patient has absent breath sounds and a rigid belly. Then, when asked, they are able to tell the staff member the value of Hank's hemoglobin. EMTs would not have that information. Paramedics also would not have that information, but would have started IVs and decompressed Hank's chest.
Walt tells Jessie that there no cell service in the underground lab ("nonexistent, We are shielded"). Yet, Jesse calls Walt from his cell phone (17:05). Jessie is actually using the lab's cordless phone, not his cell phone.
When Jesse is shown the new lab, it is often misheard that he remarks "It sure is shiny up here," leading people to believe the lab was perhaps created on an upper floor. However, Jesse actually says "it's shiny up in here," which is a slang way of saying "it's shiny in this place" having nothing to do with direction or floor level.
When Walt and the DEA agents visit the assassin in the hospital, his arms are free. As he was just involved in the attempted murder of an agent and the murder of bystanders he would have been under arrest and handcuffed to the bed frame.