In a system in which you have three branches of government and you do not want one branch to be able to completely control the others, it is inevitable that each is going to have some weaknesses and disadvantages. The legislative branch, established by Article I of the United States Constitution, is the strongest branch of government, given more enumerated powers than either of the other branches, and it still has weaknesses.
The first weakness is that of the power of the presidential veto. Congress can pass laws from now until doomsday, but the president can overrule every one with a veto. Of course, no president has done this, so far, because government would then be completely ineffective. Congress can override a veto with a two-thirds majority, too, but this is far more difficult to do in a two-party system, particularly today, when the two parties are so polarized.
The second weakness of the legislative branch is the necessity for both houses to pass any legislation. The House of Representatives can pass a bill, and the Senate can pass a bill, but unless the two versions are reconciled, there is no law. This means that the people in the House and the people in the Senate must agree to settle any differences in the bills. This can be difficult, and sometimes it is impossible. Any legislation that is not reconciled cannot be passed.
The third weakness lies in the nature of representation, which is different in the House from its nature in the Senate. In the House, each representative is representing a relatively small group of people, somewhere between a half a million and a million people. A senator, on the other hand, may represent as many as thirty or forty million people, depending on the population of the state, because a senator is expected to represent all the people in his or her state. This means that a representative and a senator have very different agendas. For the representative, it is about keeping the people in a small district happy. For the senator, it is about having to please all the people in the entire state. There are good reasons it was set up this way, but the fact is that it creates tussles between the Senate and the House because they have very different priorities and agendas.
Those are three weaknesses in the legislative branch, weaknesses that can render Congress quite ineffectual, in spite of its being the very strongest branch of government.