Lead acid batteries

It shouldn't hurt the new cells. They just won't get charged enough which is bad in the long run. But in a discharge the bad cells will easily be reverse charged which should be even more damaging. Generally folks keep all cells in a series string at the same ampere-hour rating and state of charge. That way the end points are reached by the whole string at the same time. That gives the most available ampere-hours with the least unused.
Also old cells tend to self discharge more.

 

The only cell that works good on is lithium-ion. Lead acid is not too bad. Nicad and nickel-metal hydride are history dependent. That means either a charge or discharge perturbes the voltage which slowly returns to the normal curve. Heat can make these cells drop voltage which fools a charger into burning them up.

I find that the voltage only decreases when a load is applied.

When lead acid cells get old they fall apart. The best thing to do is keep a separate string and prepare to throw them away.