IMHO My personal bugbear is the pidgeonholing that happens in the UK design market - you have to be really careful when you start out and make sure that you step into an area of graphic design that you are happy to stay in - crossing the lines is apparently taboo.
A 'graphic designer' as a general term splits into so many areas, if you get stuck in a specific field of graphic design, then that is where you are likely to stay until you die - unless you are really lucky. For example, a design agency won't look twice at you if you have a history of working in any other design environment (unless you really knock their creative socks off). If you want to be an agency designer, then you need to put your foot down, walk over the competition and become one from the outset.
If you get stuck working for Matalan you will find yourself in a rut where only similar organisations will take you on, based on your past experience. Become a typesetter or Mac-operator, then kiss your chances of ever doing any exciting design work of your own goodbye.
Magazine design (where I am stuck) is even further pidgeon-holed into categories, work on one type of publication and then you highly likely to end up working on similar ones for the rest of your life - just because I have never worked on a glossy title before, they wouldn't even look twice at me - even if I have over 10 years of experience in the industry and have designed shelf publications before. My biggest career suicide was my last job before redundancy 4 years ago as a puzzle magazine designer - apparently that is all I am good for now (was even called a 'Puzzle Queen' at an interview once...). I have been lucky though with freelance franchise magazines, but I actually can't walk into a job because I pidgeon-holed myself very badly.
Oooops, will get off my soapbox now. Please note that the above are my personal observations... and I would happily like to be proved wrong if other people have had better experiences out there