From the official writer's Tumblr account, when asked about a holiday celebrated half way through Season 1:
Asked: What date does Unity Day fall on? I'd like to know so I can party
Answer: Chronology questions have been asked a lot (usually in conjunction with ‘has Clarke had her birthday’). I finally was able to get the closest thing to an official timeline I can get from our script coordinator Ryan, who has to keep track of things like how many days/nights pass in an episode.
According to him, Season 1 was 29 days. The delinquents landed on Earth on September 13, 2149. Unity Day is October 1st.
Considering not all days are shown, and some episode span part of a day while others span multiple days, it's understandable to be confused. The Injuries are the typical Hollywood Healing and It's only a flesh wound. Jasper recovers from a spear to the chest in a week, but they did show SOME signs of complications, infection, drama so they didn't just use a reset button. He even has PTSD from it for a while.