If you applying for a grant or a fellowship that involves competing with people from other disciplines consider the suggestions below. Most of these applications are reviewed and decided by committees that comprise people from a range of disciplines, e.g. from marine biology to theoretical physics.
Remember your audience
They are mostly not in your field and they are busy and jaded. They will look over [n..b I did not say read] your application very quickly.
Count the cost of applying
These applications are actually much more work than field focused [e.g. condensed matter theory] ones. Don't kid yourself you can just cut and paste material from other applications. Don't kid your self that your "excellent" "track record" and "outstanding" "research project" will carry the day. Inevitably, you will be competing with a few individuals who will spend a lot of time carefully crafting a compelling application that does things like those below.
Kill the jargon
Not only can't non-experts understand it they may even resent your for it and rank you lower.
Less is more
Cut material out. Try and get over a few simple details and achievements.
Avoid long lists. For example, rather than a list of 10 invited conference talks, say you had 10 and give details about 3 saying why those are particularly important conferences.
Provide a clear and concise statements of your major scholarly achievements.
This is what I most desperately seek in applications, yet often don't find.
For example, if asked to list your 5 most significant publications, provide a 30 word statement
for each stating why it is significant.
Provide context for everything
[significance of project, journals, author order, citations, grants, prizes]
Outsiders don't know. You have to tell them.
For example, saying you were a finalist in the APS Leo Apker award won't mean anything and its significance will be lost. Non-mathematicians need to be told that most author lists are alphabetical and publication and citation rates in mathematics are much lower than in other fields.
Don't under-estimate the power of the joy of learning
I have noticed that even colleagues who suffer from metric madness are favourably disposed when they actually learn something new about a different field.
on the flip side, if your application makes people feel dumb that will work against you.