We know that dates are often off by 1 day because there are hidden decimals - but main source & main fix?

Just show the decimal so you know the reason why? Usually it happen when using multiple calendar with different end working hours or when updating and not paying attention on the hour when ticking started and or finished tick boxes on Status.

John, I wrote a post about it on LinkedIn on how to find these:

P6 Schedules - Activity Date / Time Issues | LinkedIn

The decimals are usually down to people entering durations to match dates, or from imports from excel, where the duration has been developed form a formula that might be from a prodcution rate etc.

The part-days is usally due to the status or activity constraint timestime being set to 00:00 instead of 08:00 or whenever the calendar start time is.

there are 2 things that do this 

#1 as you mentioned the Original durations and or remaining durations are not whole numbers.

soultion is to always make the remaining durations whole numbers.

#2 the TIMES are incorrect could be the project start time 

Actual starts and or finish TIMES

Constraint date TIMES

the data date TIME

typically all start TIMES should be 8:00 am or the earliest start time in any of your calendars

typically the finish TIMED should be 5:00 pm or the latest workig hours in all of the calendar 

This holds true for actual start, actual fininsh and constraint TIMES.

I would also eliminated the defaut 1 hours lunch time between 12:00 and 1:00

so a typical day would start at 8:00 am and finish at 4:00 pm

doing this keeps your sechedule consistant as far as dates and times are concerned. 

The decimal in the duration usally results whe you update the duration % complete and not updating the remaining duration  manually i.e. a 5 day activity that is 50% complete will yield a remaining duration of 2.5 days but without the decimal places turned on will show a whole number of 3 days remaining.