There's a big gap between how TV, movies, and books portray the CIA (where it's handy to have a super-competent, mysterious enemy for the protagonists to struggle against) and the historical realities. The CIA was only founded in 1947, with direct antecedents only going back another few years. It was still very young in the 1950s to 1970s, growing and changing bureaucratically, gaining and losing influence depending on the Director and the current President, and trying out new types of activities (not just spying, but performing covert ops).

The early success in the Iran coup gave them a lot of confidence, but probably a lot more than it should have, as there were a lot of extraneous factors that happened to line up to make that mission a 'success,' and covert ops entered the toolbox of presidents who wanted to accomplish something while maintaining deniability. Unfortunately, not very many of them went that well, in hindsight, and the Castro assassination attempts are just a few among many.

There were no professional assassins in the CIA (maybe today, though I doubt it, but certainly not then), and very little to no institutional or personal experience in managing such an operation. To their credit, the CIA recognized this and tried to contract the Castro assassinations out to the 'experts' - the mob - but that didn't work out (and is a leading theory among more historically minded JFK conspiracy types for why the mob would assassinate him eventually). At that point, they were in a situation a lot like you would be if someone gave you a lot of money and asked you to manage the assassination of a foreign leader. Where do you start? Who's going to do the killing, while maintaining deniability? Where do you even go for a competent, quiet assassin? So, they tried bribing people, and sneaking poison into food, and going for technological solutions like putting explosives in a conch shell (Castro loved diving), but it's not that surprising that these fairly amateurish attempts failed, really. Meanwhile, a lot of really smart and stubborn guys in charge were getting frustrated that they'd failed and more and more wanted to make it happen, the culmination of which was the disastrous Bay of Pigs, which was not even remotely secret and had little chance for success by the start date, but bureaucratic inertia seems to have carried it onward.

At any point the US could have dropped bombs or sent in the Marines, but that would defeat the whole point of using covert ops.

Sources: Andrew, For the President's Eyes Only; Richelson, Wizards of Langley

I hate to just list a source, but I lost my copy of this in a flood.

Psywar On Cuba has a ton of declassified documents on the anti-Communist operations of the CIA.

Like the hundreds of schemes for killing Castro, there were a lot to try to destabilize Cuba. There were ideas that dosing Castro with a drug that would make his beard fall off would cause an uprising. Plans to give him LSD before a radio address, making him sound crazy. Plans to surface a nuclear submarine off the coast of Havana and lighting off fireworks, making the Cubans think Jesus had returned and overthrowing the secular Castro regime, and more. I think most of these were never attempted, but they're interesting to read regardless.

I think comparing these wild attempts with what happened in Guatemala in 1954 is a good idea as well. CIA declassified files outline the operation pretty clearly: basically, pretend a huge uprising was under way using a clandestine radio station to announce the mythical invasion and scare away the leadership while a small decoy army (according to the document, 260 men) marched across the borders. Arbenz fled soon after the coup began and the land reforms he had begun were reversed.

In addition to what /u/Cal_history has to say:

The Intelligence Directorate, or DGI as it was known, is Cuba's equivalent to the CIA. The organization was well trained by the Soviets and had much experience operating abroad, in Panama, Angola, Grenada, etc. Cuba served as a major communications intercept site for the Soviets and succeeded in intercepting large amounts of U.S. government and military transmissions.

In addition, the DGI succeeded and still succeeds in infiltrating various U.S. government agencies and Cuban exile groups. An example - Ana Montes, a senior Cuban Analyst for the Defense Intelligence Agency was convicted in 2002 for committing espionage for nearly 30 years. source. The man who investigated her case, claims that she is just the surface of Cuban penetration into the US Government.

Basically, numerous USG operations against Cuba have been compromised by moles operating out of the U.S., either for Cuba or the Soviets. The Bay of Pigs is one particularly striking example of this.

For more, check out Clarridge's A Spy for All Seasons and Weiner's Legacy of Ashes. Should be noted that the former is the memoir of a disgraced CIA employee, so grain of salt and everything.