Were innovations (bid'ah) present during the time of the Prophet, peace and blessings be upon him, and were they widespread while he was calling to Tawhid (monotheism), knowing that the Sharia was not yet complete?

Perhaps the questioner means by "flaw" polytheism (shirk), which the Prophet, peace and blessings be upon him, was sent to eliminate and replace with monotheism (tawhid). As for innovations (bid'ah), they were not widespread among the Companions; rather, they would refer to the Prophet, peace and blessings be upon him, in all their affairs. He would strongly condemn any incorrect independent reasoning (ijtihad) in worship, as in the story of the three individuals who wished to dedicate themselves to asceticism and devotion. The Prophet, peace and blessings be upon him, rebuked them for this, explaining that he fasts and breaks his fast, prays and sleeps, and marries women, and "whoever turns away from my Sunnah is not of me."