I also thought about this too, for our first lambing this year. So I knocked up a little record sheet in Word to prompt me. Some filled in advance, some at birth and some before turn out:
Ewe name/tag
Due date/scanned for
Pen location and spray mark
Delivery date and time
Presentation of lamb(s)
Whether assistance needed
Dead/alive
Teat checks
Whether ewe bonded with lamb(s)
Lamb gender/weight
Whether had colostrum
Iodine to navel
Anus functional
Castrated
Tag number (when applied)
Name chosen
Spray mark used
Space for notes on each page, e.g. for other points, general notes on behaviour, any treatments given etc.
Lots of the points below seem eminently sensible but are about the ewe in general - not the birth or the lambs - so would be in the ewe's records. Would also log feeding details in the run up and after lambing.
I'm going to add in prompts to check eyelids (splits/entropion) and whether afterbirth has been seen.
Agree with
@Womble that knowing whether any issues are unlucky coincidence or a problem is tricky for a small flock and there are hazards in replacing numbers (i.e. bringing in new animals) that may outweigh the gains of culling for some faults in the short term.