I'm in the UK so my answers may differ from US replies.
Medically: There's a lot of knowledge missing from Doctors in the UK. The first GP I approached had no idea of where to go after my appointment, which lead to a long wait to get to a gender clinic, from which I was promptly turned away as 'not trans enough'. My current GP doesn't understand how often to run bloods to check for hormone levels and such, and doesn't seem to understand the results that he gets anyway. There's a lot of pressure on me to advocate for myself and practically hold my Doctors hand through my treatment that I don't think exists with many other treatments. It's not necessarily their fault, it's a rare enough occurence that I think many UK GPs just haven't had experience with the care of trans people.
Societal pressures: I'm still in the early stages of transition but am 'out' to everyone. There's a lot of pressure to dress a certain way and expectations to not look like a 'man in a dress', which I obviously do. Strangers think nothing of pointing and laughing at the 'weirdo' on the train. Combined with a dose of dysphoria and my day can be absolutely ruined by this kind of thing.
Better education of GPs and more public trans people. Except for Chaz Bono, I don't know anyone in real life that could name another FtM trans person. Whenever people talk about trans people I think they're thinking about Caitlyn Jenner, there are very few other trans celebrities that are very well known in the UK.
I'm not looking for anyone to 'take the bullet' for me, I don't think it's fair to expect individual trans people to become representative of the trans experience, but if 'joe public' had more examples to pick from, I feel like it could go a long way to removing the social stigma from being trans.