Is acting upon a weak hadith, such as the supplication for entering the home, "O Allah, I ask You for the best of entries...", considered a Bid'ah (innovation) and does its doer incur sin, knowing that Sheikh Al-Albani declared it weak?

It is permissible to act upon a weak hadith (definition) concerning the virtues of deeds, encouragement, and deterrence, as long as it is not fabricated, provided that its weakness is not severe, and that it falls under a general sharia (definition) principle. This is not considered an innovation. However, one must avoid weak hadiths that involve estimating or specifying a particular act of worship.