There are three things that really piss people off. I'll go in order of descending objctivity.

The first most obvious one is that the ending contains major logical plot holes. Characters appear and disappear from places with no indication of how they arrived or left or even why they do so. There are other issues that people claim to be plot holes related to the antagonist reaper's and character motivations for actions that seem nonsensical, but those are less concrete.

Second, the ending only adresses the conclusion of the reaper threat, and not the saving of the galaxy. These seem similar, but are in fact two very different things. Players built a strong connection with the characters and civilization in the mass effect universe. The ending truncates almost immediately after the reaper threat is neutralized. In the process of solving the reaper threat, all the mass relays, devices that facilitate FTL travel and connect the galactic civilization, are destroyed, stranding the massed galactic fleet in sol. In addition it's been shown prior that mass relays when destroyed release energy equivalent to a supernova. So not only does the ending not address the saving of the galaxy it at the very last minute throws it entirely into question. This is particularly frustrating because your decisions in the 3 ME games drastically shape and are informed by how a post-reaper galaxy would look. In essence the ending fails to address the true conflict of the series entirely.

Finally, the ending dishonors the themes of the mass effect series. Throughout the games, the writers have addressed ideas such as strength through unity, natural against written law, trust, and even the nature of life. The treatment of synthetic life in the series is beautiful as the once malicious robotic geth are slowly revealed to be sensitive, benevolent automotons. In contrast the ending presents the reaper's motivations: synthetic life cannot coexist with organic life, therefor, advanced organic civilizations must be eliminated before they desroy themselves. The reaper's position is simplistically luddite compared to the characterization and redemption of the geth. If the player was capable of objecting to it, that would be okay if a little strange. Instead the ending forces shepard and by extension the player to accept the reaper's premise against everything that has been established thus far. This to me is the most heartbreaking part of the ending because mass effect had done such a great treatment of classical sci-fi themes to that point, only to throw them in the bin at the very last minute.