Like Karl, I have successfully mixed old and new batteries and have even mixed AGM and flooded cells, though in separate banks rather than direct wired to each other. The relative condition is the key factor and sometimes it can be difficult to tell. It's always the safest approach to replace the entire set (even in the flashlight example) because a "fair" battery will quickly suck the power (and maybe some of the lifespan) from a "good" new battery.
The "replace 'em all" rule is aimed at the average consumer who isn't into battery testing/monitoring and just wants things to work reliably when he turns the switch on. It's "good practice" but not absolutely necessary. As with most technical things, the general rules can be violated
if you know what you are doing, know the signs of a potential problem and keep an eye out for those signs. For wet cell batteries, you can check the specific gravity of each cell to determine to the battery is in sound operating condition. If it has a weak cell, I would not couple it with a new battery, but if the cells all test decently I would not worry about combining them.
I might add that the com-bined voltage of each set is always matches.
It has to if they are wired in series - the good battery is dragged down by the poorer one, reducing the overall voltage in that set. It functions as a single battery when wired that way.
Are you saying that the batteries test out at different voltages (when disconnected from each other, of course)? That's not a good sign. Surely the new ones were all the same when you installed them. How long ago was that? You cannot reliably measure the voltage in one battery if it is wired to another, whether series or parallel. To get an accurate reading on a single battery, you must disconnect it from the others.
Corrosion at the posts or bad wiring between batteries (e.g. corrosion under the terminals where they clamp to the wire) can cause strange things to happen in both charging and discharging. Wonder if you have a bad wire somewhere?