More specifically, the lack of observable gradual change between species.
Most significant phenotype differences occur over several thousand generations, which means several thousand years on up. While we certainly can create experiments where a controlled form of evolution occurs within a very small time-frame, I'm going to assume that you're not interested in closed laboratory experiments given the nature of your question.
It obviously has a strong connection with a normal shark, but where's the "half-hammerhead" shark? Where's the species that only has a SLIGHTLY wider head?
The data below does answer you question, but in reverse. Hammerheads are much older than most of their relatives; so their cousins have actually grown smaller heads... but there are certainly intermediates.
From Andrew Martin (1993 - mtDNA data) via Elasmo-research.org:
*The circles represent the head-width vs. body-length ratio.
Martin's conclusion: "...the hammer appeared rather suddenly and fully formed, and was later optimized along different lines to suit various selection pressures."
I really doubt that a single mutation on a normal shark resulted in a head shaped like that, it had to happen gradually. Right?
Not necessarily. Single Nucleotide Polymorphisms (a.k.a. - "SNPs" - a change in one nucleotide) can have pretty wide-ranging effects.
The vast majority of humans, for instance, are lactose intolerant in adulthood. However, lactose tolerance evolved twice from two different SNPs in two different human populations: One European and one African. One gene. One regulatory mechanism change. Massive benefits (essentially opening up a whole new resource in adulthood).
Significant differences in phenotypes (the physical appearance of something) can require more gene mutations, or not. It depends on where the mutation is in the genome and what the gene does.
But if it was for whatever reason beneficial to have a slightly wider head, why don't all the sharks have slightly wider heads now?
The simple answer is because either there wasn't enough selective pressure that the rest of the shark phenotypes succumbed to that the hammerhead avoided, or that the hammerhead design doesn't give enough of an advantage to completely dominate the gene pool. An alternate, but more abstract answer, is that there simply hasn't been enough time for the hammerhead design to dominate the shark phenotype. Remember, evolution works by generations - not years. It would take unknown thousands of generations for a weakly-advantageous design to dominate an entire niche - if it ever would.
Also, it is worth it to point out that evolution doesn't only select for advantageous mutations. Mutations that aren't very detrimental can still exist within a population as long as the detriment doesn't prevent resource exploitation and offspring production. Think Huntington's Disease which severely restricts a person's survivability, but only after their mid-30's (in general) - plenty of time for the person to have sex and raise a kid into semi-adulthood. It is a genetic defect which sticks around only because it allows humans to reproduce before it seriously affects them.
The original ancestor certainly didn't, and I'm sure that if it's child only bled slightly from it's eyes it wouldn't really help if much in life.
Maybe, maybe not. Maybe it shot something else before blood, and then a mutation caused it to shoot blood instead - but the overall effect (deterring predators) was the same so it doesn't really matter.
You're correct that some traits might appear very awkward if they had evolved gradually, but the question then becomes: Did they evolve gradually? Sometimes we simply do not know.
So why did the inbetweeners survive long enough to evolve even more, and why did they THEN die out?
Like I said above, just because a trait is detrimental doesn't necessarily mean it will be eliminated. As long as the being can survive long enough to reproduce successfully with the trait, the trait might not be eliminated for a very, very long time- if ever.
As for in-betweeners dying out - it's difficult to think of it like that. You're talking bout LCAs ("Last Common Ancestors") of extant (currently-living) species. While some LCAs just die out for some reason or another, it's more common that the LCA simply continued to evolve and become a genetic relative due to some sort of isolation.
Think of it like the in-betweeners coming to a fork in the road. Some choose right, some choose left. There isn't anybody left behind - merely two populations that are changing over time that were once one group until they don't really mate between each other anymore (or can't). Heck, even Biologists have trouble deciding at what point a population is considered a different "species" because of discoveries in the last 50 years - so right now a firm answer like "It takes 15% of the genome to change for a new species to emerge" isn't possible as it doesn't really work like that.
We'll get to it eventually, but for the time-being, it might be easier to say that everything currently living on Earth is an in-betweener of something else in the future. Everything in its current iteration will eventually die off, but not before something else emerges from our offspring which may or may not be significantly different from us due to however many genetic mutations our offspring have from us. It could be one that opens up a whole new realm of possibilities (like lactose tolerance) or an accumulation due to selective pressures (like Phoemelanin production and pale skin in humans [Redheads] to produce more Vitamin D3 at higher latitudes).