Imagine two animals, believed to be related. Let's call them A1 and A2, where A1 is the ancestor species.
A1 -> A2
Now from the idea of common descent, we should expect to find somewhere in the fossil record an individual who shared some features with both A1 and A2, a transitional fossil, a missing link if you will. Let's assume we find this example and call it A3.
A1 -> A3 -> A2
Now somewhere in the FR, after A1 but before A3, we might expect to find another transitional form, and ditto for A3 and A2, so now we have two missing links. Let's assume we find them too.
A1 -> A4 -> A3 -> A5 -> A2
Now, of course, we have 4 missing links, but some really good field work turns up three of them.
A1 -> A6 -> A4 -> A7 -> A3 -> A8 -> A5 -> ? -> A2
Now a reasonable, logical and scientific mind would say that's a pretty confirmed theory. Particularly if half of these transitional forms had turned up because people had used the theory to make educated guesses about where to look. I mean, what sort of perverse idiot is going to look at a series of successes like that and say "Ah, you never found A9, it must all be a load of hooey!"
Apart from BC and his 'geology professor' (hint: BC, ask a palaeontology professor next time), obviously.
N.B. (1) See how the number of 'missing links' went from 1 to 2 to 4? The more fossils we find and fit into a series or tree, the more gaps we create, so if there are 'masses of missing links' it's because we have so much evidence to begin with. (2) Even if they never turn up, it doesn't disprove evolution as there is plenty of positive evidence to evolution around to go on. So an absence of evidence isn't only not evidence of absence, it doesn't even particularly disconfirm the theory, as where there is evidence it is supportive.
No there isn't an unbroken string of evidence from ape to man, and no we don't particularly care. Science doesn't work that way, so the requirement that it does is just a strawman set up to deceive the credulous.