Opinionations.
Of course they ****ed up, people are dead. Whether that was their intention or not is debatable.
In general, the situation between Israel and Palestina (and the surrounding countries) has been ****ed up by everyone involved. The core of the most recent problems lies in colonial history of the area and the decisions made after the WWII, which injected the state of Israel into existence on very shallow grounds right on top of an area that was already inhabited by another group of people, namely the palestinians (arabs). Obviously, this has proved time and again to have been a Bad Idea.
However the blame seeking game is something that never typically helps in conflicts like this, since there's been too much time passed and blood spilled, and no one is willing or able to back up.
The most ironic thing is that the two sides in the conflict are more alike than either wants to admit.
On the Israeli side, we have people who have been displaced, shoved around, told what to do, constrained in movement and other freedoms and subjected to mass killings - a few generations ago. Then they were given their own state, location defined by their holy texts (!). In my opinion, these are at best dubious justifications for the existence of Israel as a state, but be that as it may they do exist now as a nation and a country, and their government and military have the obligation to do their best to protect their population in a situation where collateral damage is nearly impossible to avoid. There must be a lot of frustration going on there.
On the Palestinian side, we have people who have been displaced, shoved around, told what to do, constrained in movement and other freedoms (whether it be with good reason or no), have very low standards of living, limited supplies, limited infrastructure and a rotten leadership that is not helping the situation AT ALL.
As I see it, it's a Catch-22 situation at worst.
To reduce the overall tension on the area, Israel wold be required to lift their embargo and other regulations, giving the Palestinian areas more of an autonomous regime.
However, they cannot do that as it would arguably lead to increased terrorist activity and deaths of Israeli citizens. They would need to observe clear reduction in the support to Hamas and Fatah before easing up on the Gaza strip and West Bank.
Obviously, the population's support to Hamas and Fatah is unlikely to continue as long as Israeli forces are there to provide easy targets for propaganda and to act as the embodiment of the oppression (perceived or intentional) of the Palestinian people. So, the acts of terrorism will continue as long as Israel is perceived as a threat, but Israel can't back off before acts of terrorism stop or reduce significantly.
So, there aren't easy solutions and neither side is free of wrongdoing in my eyes.
However I would say that it's not impossible to solve the situation. Northern Ireland was a real mess a few decades ago. Generational/cultural memory is a real curse in cases like this...