The biggest disadvantage to being and aerospace engineer is all the work you need to put into it upfront in college. The jobs themselves are exciting and rewarding and will be "easy" by comparison if you study at the right school. For reference, I revived my Aerospace degree from Georgia Tech and no job I have ever had has been as tough as that place. At the end of the day I a was better for it. Also, the best colleges will offer Internship and/or Co-Operative education opportunities which is a must in my personal opinion. There is NO "shrinking" job market as some answers may suggests. Aviation globally is in the $100s of billions and growing every year lead by the US. However, depending on what you may want to focus on job-wise, the openings may not necessarily be in the United States. Hopefully you see this as a huge plus since getting out and seeing the world is one of the major benefits we all enjoy thanks to aerospace engineers and the whole aviation community. Also, eventually these jobs will transition into Space thanks to companies leading the way like Space X, Blue Origin and Scaled Composites.
Speaking on $pay$, most aerospace jobs are middle to high earning potential (for engineering) depending on where you live/work and what you focus on career-wise. AE jobs in California pay great, but the cost of living is ridiculous while AE jobs in GA pay O.K. but the cost of living is pretty fair.