It depends on the gene that caused the tail-less-ness.
The Manx gene is a dominant gene and is often, but not always, associated with significant problems.
The bobtail gene is recessive and is not associated with any physical problems. Bobtail cats are no more likely to have physical problems than their normal-tailed counterparts.
Because of the physical problems associated with the Manx gene, it is much more likely that a random-bred tail-less cat is manifesting the bobtail gene.
An easy way to tell is that bobtail cats do have a bit of a tail. It's just very short - only an inch or two long.
Genetically, it's not really possible to tell based on a ratio of 50:50 tailed/tailless kittens. Just based on this, it is equally likely that Dad has two recessive bobtail genes (short/no tail) and Mom has one bobtail gene and one "tail" gene (normal tail), or
that Dad has one dominant Manx gene and one "tail" gene (short/no tail) and Mom has two "tail" genes (normal tail). Either combination would statistically give you 50% tail-less kittens and 50% normal tailed kittens.
The good news is that, regardless of what gene the kittens have, if there were problems you would probably know about them by now. Incontinence is a very common problem with Manx cats. Another common problem with Manx kittens is anal and/or urinary atresia, which basically means that the kitten is born without an anus and/or urethra. Obviously this is a birth defect that is not compatible with life and affected kittens die within the first week or less.
I recently fostered an adorable bobtail kitten. He was very vocal, probably in part because cats use their tails a lot to communicate and he didn't have that option. But I told him that he shouldn't be ashamed just because his tail is only an inch and a half long. After all, I don't have a tail at all!