I used to have a great deal to do with applications for postgraduate taught courses (as an administrator, not an academic). What I'm about to say may not apply to all academic areas so for context, this was for a course in an area of applied psychology.
In our department, we looked mostly at the applicant's academic record (degree result achieved/predicted, backed up by transcript) and their academic references. It goes, I hope, without saying that you should choose your academic referees with care and discuss the application with them before you go ahead. It never looked good when we got a reference back from someone who made a point of saying 'I cannot comment on the applicant's motivation for applying as s/he has not discussed this with me'. On one memorable occasion we got a reference from an academic who said although the applicant was from her department they had never had any contact and she had no idea why she had been nominated.
For many of our more mature applicants who had been away from study for a long time, work record was very important, supported by professional references and evidence of financial sponsorship/paid study leave from an employer.
Where applicants were interviewed, this carried a lot of weight.
I'm afraid the personal statement was perhaps the least most important bit of the application. I did get rather tired of reading about 'passion' and many applicants (especially from overseas) took 'personal' very literally and provided some quite inappropriate personal information. People with a very good CV needed to write very little in the personal statement because it was so obvious why they would be good candidates.
Having said that, I think it's important to make an effort with the personal statement, especially if your application is an unusual one (e.g. you are older than the average applicant or have an unusual first degree). Someone with a genuine case for special consideration, e.g. who got a 2.2 but had very strong mitigating circumstances, which an academic referee verifies, should put particular effort into a personal statement. Don't gloss over any difficulties and hope they won't get noticed. We once had an application from someone with a 3rd who made no attempt to explain why he hadn't done better. Not a good idea.
I would stress that you need to come across as genuinely keen but also realistic and well-read in the subject. Please, please get somebody to proofread it if you're not 100% confident about your spelling and grammar.
Also, if you apply to more than one place don't re-use the identical personal statement in all the applications! We once had someone who said 'I have been to many open days and reviewed lots of prospectuses and I am confident that the place I want to study is Nottingham Trent University.' Lovely. Just one problem: my university wasn't Nottingham Trent.
Good luck!