One of the issues I've noticed over time is a lot of instructors have an abundance of technical skills without the people skills / customer service skills to back it up. Also, nobody wants to hire the typical "timebuilding" instructor who isn't enthusiastic about flying or teaching.
So I'd say those are the two things that would impress me with a resume. Showing some sort of familiarity with customer service would be a big plus, like if you've ever worked in other jobs that deal with the public or customer service in some way. Also, somehow show that you're excited about flying and/or teaching. Been involved with any aviation clubs in school? Volunteered with the EAA? Member of AOPA? Helped organize a fly-in? Have a collection of aviation photography? Anything like that, that shows you care about more than just moving up the ladder, would be a big plus.
Being able to fly an ILS down to minimums means little in the instructional world, whereas people skills are worth their weight in gold.
Just my $0.02.