Some of these objections are more subtle than the ones that Descartes responded to (e.g. to do with the notion of cause and the I), however there are a few points where the objections are related or similar:
1) & 2): A number of objectors (Hobbes, Arnauld, Mersenne) point out that the identity of the "I" is still an open question, for it could be that what is being referred to is the physical brain (and not the mind). Thus, thinking may be a physiological process determined by the physical brain. Descartes''s response here is twofold: firstly, he says that we clearly and distinctly perceive of mind and body as separate substances, so they must be so; secondly, whilst - he admits - there is a close interaction between mind and brain (brain damage impairs thought), it is possible for the mind to exist separately.
4) Mersenne objects that Descartes cannot say "I think therefore I am" without first knowing what thinking and existence are. Descartes''s response to this is to argue that the Cogito is a direct perception of a truth, and not a string of reasoning involving definitions.
As you can see, Descartes - or the objetors - don''t really investigate the possibility that there might be multiple I''s. The closest they get is to question its existence in general, or to suggest that the brain may be as much a part of "I" as the mind. Also, the notion of cause is only partly dealt with in that it is wondered what the cause of thought is (i.e. the brain or the mind). Remember: Hume''s scepticism regarding causation come later, so it is generally assumed that causation is not a problematic concept. Nietzsche''s point that causation is perhaps a human construct is therefore not entertained.
To defend Descartes slightly, I think that there is something that can be rescued from the Cogito. It may not, as Nietzsche points out, guarantee the existence of the separate "I", or provide evidence for dualism, but it may prove simply that our mental experience is not reducible to physical descriptions. In other words, my experience of the world cannot form part of a certain type of objective picture of reality.
Anyway, that''s just take on it - any thoughts are welcome.