Overall the show doesn't have sad endings for MAIN characters (it's not over yet), but there are many emergencies that have sad endings for the minor characters involved.
As of now, no main character has died, there have been a couple side characters who have (such as Abby's mom and Shannon Diaz).
Shannon Diaz leaves Christopher with Eddie before his character is introduced, this is mentioned multiple times. Multiple emergencies involve child abandonment.
From 2x11 through episode 2x13, there are some graphic depictions of domestic abuse. Maddie's ex-husband Doug is extremely abusive and there are allusions to this throughout the show.
In my opinion it gets a bit excessive, lots of blood and horrible injuries. The show is TV-14 but some of the episodes push it a bit with the gore. Some of it is clearly fake but some is pretty realistic. However the show is mainly lighthearted, so it's balanced out.
I don't think there's cutting in regards to self-harm, if there is it's not graphic. Shaving is shown a few times though and there may be accidents involving razors (not sure).
Multiple broken bones throughout the show, some are pretty graphic. Buck's leg is crushed by a fire truck in 2x18, and this is a major plot point throughout season 3.
It's rare and easily skippable but it does happen in a few episodes.
The ones I can remember:
- 2x12: Chimney Begins (skip when Chim is being trained by the paramedic) - 4x06: Jinx (skip when the girl gets her head stuck in a lion mask, this one is barely visible though)
I know there's also one in season 1 but I can't remember what episode.
May Grant attempts suicide by overdosing in the first season, and it's discussed again in season 4. It's non-graphic but you do see the scene where she is found after the attempt and taken to the hospital. Maddie Buckley attempts suicide in either season 4 or 5, and suffers from post-partum depression.
No slurs, but there is homophobia. Hen and Karen experience some I believe (they are a black lesbian couple). Josh (a gay character) experiences a hate crime but it's not graphically shown. Some conversations about Michael (a black gay man) could be seen as homophobic.
A few LGBTQ main characters come close but they make it through, don't worry! (I'm not sure about characters on calls but none stand out to me so I don't think it's a major thing.)
Buck and Abby's relationship is a large age gap (he's 26 and Abby is in her mid-forties), they're only a thing in the first season and it's talked about in later seasons.
(It's also good to mention that the actor for Buck was 26 at the time and the actor for Abby was 49-50.)
There are many emergencies involving people drowning/trapped in water.
In the tsunami episodes (3x02-3x03) there are many dead bodies shown in the water and a few instances where characters gasp for air or almost drown. Maddie tries to commit suicide by drowning herself.