Were the Prophets free from any shortcomings? I do not mean anything that may be disrespectful to a Prophet; I mean things like physical problems and things like forgetfulness etc.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

The Prophets are free of physical defects and the like. Al-ʻIraaqi wrote:
"Al-Qaadhi ʻIyaadh said, 'The Prophets are free of physical and moral defects and any other shortcomings. What some historians, who have no verified knowledge in this field, said regarding some of the Prophets, attributing deficiencies and defects to them, should be ignored. Allah, the Exalted, decreed that they are free of all kinds of deficiencies or defects that cause aversion of the people's hearts and eyes.' An-Nawawi and Al-Qurtubi made similar statements." [At-Tarh wa At-Tathreeb, 2/228]

As for forgetfulness, it may happen to them, as indicated in the verse that reads (what means): {And We had already taken a promise from Adam before, but he forgot; and We found not in him determination.} [Quran 20:115]

Moreover, the Prophet, sallallahu ‘alayhi wa sallam, said, "I am only a human being, and I forget just as you forget; so if I forget, remind me." [Al-Bukhaari and Muslim]

An-Nawawi wrote:

"The Prophet's statement: 'I am a human being and I forget as you do; so if I forget, remind me,' is proof that it is possible that the Prophet would forget something regarding religious rulings, and this is the view of the majority of the scholars, and it conforms to the apparent indication of the Quranic verses and ahaadeeth in this regard; however, they unanimously agreed that the act of forgetfulness on part of the Prophet, sallallahu ‘alayhi wa sallam, in this case does not go uncorrected; rather, Allah informs him of it (and he corrects it) ... Some scholars held that it is inconceivable that the Prophet, sallallahu ‘alayhi wa sallam, should be prone to forgetfulness with regard to his informative actions and worship, and they unanimously agreed that it is inconceivable that he forgets with regard to his informative statements, and they answered to the situations brought forth in this regard. Abu Is-haaq Al-Isfiraayeeni inclined towards this view. The correct view in this regard is the first; that is because forgetfulness does not contradict the status of Prophethood, and that as long as it does not go uncorrected, it causes no harm. Rather, it brings forth a benefit which is to clarify the rulings of forgetfulness (in acts of worsip) and to emphasize the religious rulings.

Al-Qaadhi said: 'They held different views regarding the possibility of his forgetting in the matters that are not related to conveying the message and clarifying the religious rulings, like his acts, habits and remembrances of his heart. However, with regard to forgetting in the informative sayings, then this is impossible for him according the consensus of the scholars. They also unanimously agreed that it is inconceivable that he deliberately commits that. As for forgetfulness in his sayings related to the worldly matters and other matters that are not related to conveying the message, like his sayings which are not related to the religious rulings or the information about the Hereafter or the divine revelation, then some scholars held that it is possible, as this is harmless.'  

Al-Qaadhi said: There is no doubt that the most likely correct view in this regard is that it is inconceivable that the Prophets do acts of forgetfulness regarding their sayings (the divine message they convey to their people); it is inconceivable that the Prophets of Allah commit a mistake in their sayings either deliberately or by mistake, whether in sickness or in health, or while calm or angry. 

The Sunnah of the Prophet, sallallahu ‘alayhi wa sallam, best testifies to this; the sayings and actions of the Prophet, sallallahu ‘alayhi wa sallam, were keenly preserved, documented, and related by those who believe in them, those who disbelieve in them, and those who harbor doubts about them, and none argued that he made a mistake in any of his sayings or actions or acknowledged that he committed acts of forgetfulness (in conveying the divine message to the people). Had there been any authentic incidents of forgetfulness or mistakes, they would have been documented, like his missing a prayer due to oversleeping, correcting his opinion regarding cross-pollinating the date palms, and choosing to camp in the nearest part of the wells of Badr...'"

Allah knows best.