I wrote a good answer, but now there's no question to go with it. Posting the answer anyway.
The original question was about placing date and time as headings for scene changes in a manuscript. It asked for any thoughts and input. Here's mine. Let me know yours.
Timing helps raise tension/suspense. We're all familiar with the countdown ticking bomb motif. It's a good plot device for the affect you want to impart to your reader. The numbers have purpose.
Timing helps establish milieu. If your world is one of clockwork precision and automaton-like, Orwellian people, then numbers and time help solidify that in the reader's mind. They have a clear purpose.
Dates help maintain chronological order for the reader. If the main character is having constant flashbacks that can't easily be delineated by italics, setting or perceptual devices, date and time are easy devices to help keep the reader straight. Again, the purpose is to aid the reader's clarity or emotional involvement.
However, placing dates rather than a blank line between scenes, if they have no clear purpose, may tend to kick a reader out of a story. Be aware that cold numbers may stand out as the uncovered pieces of story framework.
In all cases, numbers and dates should have story significance. If they do not augment the story, they will surely detract from it and run the risk of interfering with the read.
Ask a few questions of the people who might have a problem with timing and numbers. Neil Gaiman writes that (I'm paraphrasing), "The reader is always right when they say something is wrong, but they're never right about what's wrong." (Sorry to Mr. Gaiman if I botched it) Figure out what is going on with the story that is messing with the perceptions of a large percentage of readers and fix it.
Perhaps all that is needed instead of times or dates is to work in a little more time sense to the setting: shadows lengthening, wildlife changing from day to night, human activity building (rush hour) or diminishing (restaurants closing), the relative disrepair of clothing, hair and makeup, weather building, storming and clearing. Many devices indicate the passage of time. Think up a fresh one that aids characterization.