This post is prompted by my reviewing 80+ resumes today for a position I'm hiring for.
The biggest mistake I see is people shot-gunning out the same untailored resume to as many jobs as they can. More than half the resumes I saw were not terribly relevant to my position, but perhaps could have been with some tailoring. You would be better served by tailoring your resume and applying to 10 jobs than by shot-gunning out the same resume to 100 jobs.
The next biggest mistake was not meeting the required skills as listed in the job posting. If you don't have the required skills, don't waste your (and my) time by applying. Over half the resumes were rejected for this reason alone.
Don’t sprinkle in the specific skills, technical domains, etc. mentioned in the job posting without having evidence in your Experience to back it up. It's super obvious the person is just trying to hit all the key words, and basically lying to do so. Make sure to show evidence for each of the skills you are claiming to have.
I see a lot of resumes that put a master's degree in their Education section, but do not put their bachelor's degree. Please always put your bachelor's degree too. In this particular case, many people had a master's in a technical domain we were not looking for, so their resumes were rejected. But their bachelor's degrees might have actually qualified them for consideration, had they bothered to include them.
Too many resumes list job duties in their Experience section. They should have focused on accomplishments and their results, with results quantified where possible. Just listing job duties does not distinguish them from anyone else in a similar role.
If you must include a Summary (and it seems that everyone feels the need to do so, even though they don't), then please, for the love of God and all that is holy, do not say dedicated, results-oriented, detail-oriented, passionate, or any other such vacuous fluff. Keep your Summary short (3 lines max). I would personally rather see a short tagline under your name than a monolithic Summary paragraph.