How has RAeS helped my career ?
Well the career centre certainly hasn't - for no better or worse reason than that I've never attempted to make use of it. BGPM's comment's about are similar to others I've heard, but having no personal experience I can't really comment.
The Young Members Board (YMB) has a scheme for placing newcomers to the professions like you chaps on the specialist committees. I know, for example, one young Engineer who got a stint on the Airworthiness committee as a fresh graduate, which I don't think was irrelevant to his subsequently getting a job in Airbus' airworthiness department. (No, I didn't do that either, I don't think that the scheme existed when I graduated.)
Regular attendance at society branch lectures helped me a lot in my early job hunting stages - partly from the chance to informally meet significant industry people before/after lectures, but mostly for gaining a good insight into what the industry was doing - both to help steer job hunting and give me some valuable interview material.
Job interviews - we all know that if you really want a job then at-least a week's in-dept preparation is needed for the interview, probably several weeks for a first graduate job (and speaking as an occasional job interviewer, there's nothing more frustrating than the large number of applicants who don't bother). There can't be many such interviews where the 4HP library can't set you up with enough material to handle yourself as well as possible, with any interview board.
Although technically main society membership isn't a pre-requisite (it does help) being involved in your local branch will also help your exposure to career opportunities. The local branch committee are probably the great and good of your local industry - if they've worked with you on branch stuff, consider you an able chap (or chappess) and know there's a job going in your line (and if they don't, who will ?) you may well benefit.
The magazine is useful again for interview material - although the jobs section is mediocre (having checked once, not many organisations can afford the ludicrous advertising fees!).
Attending relevant society events has helped me a lot. I'm personally a light aircraft specialist and largely through the society I've become on friendly terms with people like Darrol Stinton, Ann Welch (RIP), Dick Stratton, Francis Donaldson, John Edgley, Guy Gratton -industry household names with whom regular contact has allowed me to get what I was trying to achieve done and that has reflected on my career achievements.
So, broadly that's how it's helped me. A lot of it is ultimately "self-help" stuff; just like (select deity of your choice), the RAeS helps those who help themselves.
G