We will only scratch the surface of the scholarship on whether one is obligated for geneiva b’shogeg, and we will relate to some of the issues that you raise.
The K’tzot HaChoshen[2] is among those who posit that a ganav b’shogeg is exempt from responsibility to pay if something happens to the object. He infers this from Rishonim, but his main rationale is based on an inference from a pasuk. He explains that the concept of culpability for accidental financial harm to one’s friend is limited to a mazik, one who physically damages another’s property, because that culpability is derived from a pasuk specifically regarding a mazik; the liability is not extended to other causes of obligation. Thus, if one accidentally takes another’s object without damaging it and then something happens to it through oness, he is not responsible to pay for it. Of course, he has to return the object when he finds out the truth, but if it was lost, damaged, or passed on to someone else in the interim, the accidental thief is not held responsible.
The Machaneh Ephrayim[3] presents various opinions among the Rishonim, but he agrees with those who obligate a ganav b’shogeg. One of the strong indications that he relies upon to decide that geneiva b’shogeg is obligated to pay is a gemara[4] concerning payment made by one who accidentally ate teruma. The gemara says that if the food’s price went down after he ate it, he nevertheless pays the higher price of the time that he ate it, because “it is no less than one who steals.”
Let us now discuss your question about the need for intention. The gemara[5] indeed speaks of a kinyan (an act of acquisition) as a necessary step in defining a ganav and his subsequent obligations, and kinyanim require a certain level of intent. However, the intent needed for a kinyan regarding geneiva is not identical with the intent needed to acquire in general. For example, if one lifted up an object that was in his way with the intention to relocate it nearby, he would clearly neither acquire it nor be considered to be stealing it. But if he wanted to use the object without ever returning it, this would be considered intention for theft even if he tried to be clever by having in mind to “not acquire it.” Furthermore, even one who intended to briefly borrow something without permission is considered a ganav.[6]
The Machaneh Ephrayim makes a relevant fundamental distinction. One may be culpable for geneiva b’shogeg when he intended to bring the object from another’s “possession” into his own. Such cases would include unknowingly buying a stolen object or even borrowing an object from someone who is not its owner. However, if one thought that the object that he was taking was his own, such that he did not intend to make any change, this would not be considered an act of stealing.[7] According to this, the accidental coat-switcher is not even a ganav b’shogeg and does not have, as of the time that he took the object, the accompanying responsibilities for its welfare.
The Marcheshet[8] posits that a ganav b’shogeg has the basic obligations of a ganav. In fact, he views the very source cited by the K’tzot HaChoshen to exempt a ganav b’shogeg – the obligation of an unintentional mazik – to obligate him as a ganav. Whereas the K’tzot interpreted the pasuk’s specific reference to a mazik as implying an exclusion of other forms of unintentional causes, the Marcheshet views the mazik as a prototype to actually obligate a ganav b’shogeg. If mazik is the model, then just as a mazik is exempt b’oness (under extenuating circumstances), a ganav b’oness is also exempt. In our case, taking another’s coat is usually shogeg rather than oness. Thus, according to this approach, it could be considered geneiva. Regarding intention, the coat-switcher does intend to use something that turned out to actually belong to someone else.
All agree that the disqualifications of a ganav (e.g., from suitability to testify) do not apply to an individual who accidentally took someone else’s object. Kefel is never levied in our days, and it is thus not discussed much by poskim. However, logic and implicit statements indicate that this k’nas (penalty) of the Torah, which applies in a limited manner (e.g., to only certain types of theft and only when one is exposed by witnesses) is predicated on full culpability and does not apply b’shogeg.