Say what the summary is for
A summary for deciding whether to read the full document is different from a summary that replaces it. Specify which you want.
State the audience and the length. "Six bullet points for a manager who will not read the report" produces a very different and more useful result than "summarise this".
Protect the qualifications
The most common summary error is turning "the results suggest a possible link in a small sample" into "the study shows a link". Ask explicitly for hedges, sample sizes and limitations to be retained.
Ask for numbers to be carried over verbatim rather than described.
Work in sections for long inputs
Summarise chapter by chapter, then summarise the summaries. This keeps detail from being lost in the middle of a long document, where it is dropped most often.
Keep the section summaries; they are frequently more useful than the final one.
Check before you circulate
Take each claim in the summary and find it in the source. Anything you cannot locate is either invented or inferred, and both need fixing.
Note what the summary omitted as well as what it included. Omissions are invisible and often more consequential than errors.