Should one offer to take over a lecture that the lecturer is struggling to teach?
Perhaps the best approach would be to ask leading questions that helps the lecturer head in the right direction. Or, offer an answer to a question that wasn't going well.
I've taught classes (especially ones that use complex libraries, such as parts of a game engine, that I wasn't a seasoned expert with), and have had students who had more experience with a specific topic chime in to the discussion with details I didn't know. It was great. I've also had students who were aggressive and conveyed arrogance and had them derail the class by setting up a me vs them dynamic. Not so great.
The most important thing is classroom dynamics: let the lecturer retain control (ie. facilitate the discussion) but you actively participate. The lecturer should be there to create a learning environment, not bestow knowledge on the class. You can make it clear you know the topic, and let them have you participate as much as they are comfortable.
Asking to "take over" would not go over well; offering your knowledge on bits and pieces and nudging the lecturer in the right direction through questions would be better.
No, you should not.
The lecturer isn't trying to give a single lecture, but deliver a complete course. That means connecting many lectures together, alongside supplementary material (notes, textbooks, etc), whilst pitching it at a level so that all can engage (taking into account the background and prior knowledge of all).
It may be that the lecturer really didn't understand the material. Or it may be that the material was difficult to teach coherently with the rest of the course, in a way that matched the expected prior knowledge of the others in the room.
It's most likely that your first impression is right: the lecturer was poorly prepared. But unless you're truly confident that you could explain the material to all in the room (you know all their background knowledge?), and link it to the rest of the course (you know how future lessons will be delivered and approached?), you can't expect to do better in the context of the whole course.
You should also keep in mind the reactions of other students in the class. Most people are aware that what you propose (getting up, telling the lecturer they don't understand the material, and starting to teach it yourself) is wildly inappropriate. This will almost certainly earn you a reputation you don't want to have, both with teaching staff and other students.
Your concern about balancing the needs of students to learn with the ego of the lecturer is noble, but you taking over the lecture is not only rude (or socially awkward at best), it's probably going to be ineffective. There's a high chance that other students will be turned off from the lecture based on your behaviour, no matter how technically accurate the content. Behaviour management in the classroom would be difficult after such an interruption. And as others have commented, knowing the material and being able to teach it effectively to a large group are very different things (I have tutored 1-on-1/in small groups as well as in larger classrooms, and they are very different environments).
In the immediate situation, do what other answerers have suggested and ask leading/clarifying questions in situations where you know the material is clearly wrong. If it's more a matter of ineffectual lecturing style and you just think the material could be explained better, perhaps you could start a study group or similar, to help other students to understand the material without embarrassing the lecturer?