DON'T PUT YOURSELF DOWN
I've noticed a lot of people seem to start their job applications with 'I know I'm not qualified, but...' There's nothing wrong with honesty, and telling lies about your skills and qualifications is never a good idea (way too easy to get caught out later), but why would you lead with what you can't do? If you feel like you're overreaching and applying for something you can't handle, maybe it's not the right job for you. But if you think you can do it, and still want to apply, try focusing on the skills you do have instead; the lack of relevant qualifications will be clear on your CV but if you've already impressed them by then they might still give you a shot.
Ever heard the expression, 'Nice guys finish last'? Not true. Yes, sometimes you have to think about your own interests before other people's, but that doesn't mean you get to be arrogant or pushy. I keep saying it but remember your application, and following correspondence, is going to be read and responded to by a real person, who might be your colleague one day. So be nice to them! They're not obliged to hire you just because you meet all the criteria. Definitely don't throw a strop if they ask you to complete a task before the interview stage - there'll be a good reason (probably to help them filter applications) and you'll do yourself no favours by being a diva and refusing to do it.
GET YOUR CONTACT DETAILS RIGHT
Make sure the details on your CV are correct and up to date. If you've changed your email address or phone number, you might miss an important message following up on your application or even inviting you to interview. A busy recruiter is unlikely to waste time trying to find out the right information unless they're desperate to meet you.
And it's not just your CV - if you're applying for jobs through a third party site like Reed or Monster, check your account details are correct there too. The messages received with applications are set up so employers can just hit 'reply' to contact you, and they use the email address from your account, not your CV.
MAKE YOUR CV STAND OUT
I already mentioned making sure your CV is well laid out and there are no mistakes. But even if it's perfect you still need to make it stand out. This probably depends on the kind of job you're applying for, but in a lot of cases you don't have to use Times New Roman font; there are a lot of fonts to choose from (just make sure you pick something legible) and don't be afraid to use colour either. In particular if you're applying for a job requiring design skills or creativity, make your CV attractive. It doesn't have to be a straight text document - you can use images or even include a link or QR code to an online resume.
You also don't have to send the same CV to every company; you can adapt it to suit the job you're applying for. In particular, use the personal statement at the start to explain not only what you can do but how you feel that can be valuable in this particular type of role.
Recruiters only have a few seconds to spend on each application, so make sure you include the important information you want them to know as briefly as possible. And that's all I have to say about that ;)
I hope these (and the other tips I've shared) are helpful and although I might not be posting again for a while, I'll still be checking comments so please feel free to share any success stories!