The core difference between LDS doctrine and Protestantism really is the core of Mormonism. Protestants believe that the Church as established by Christ fell into apostasy and needed to be reformed, requiring a return to the true doctrine of Jesus Christ by adhering closely to the doctrines described in the Bible.
Latter-Day Saints, on the other hand, fundamentally reject the idea that it is possible for such a reformation to be successful, believing instead that that which was established directly by the hand of God can only be restored the same way, not by the understanding of men, however sincere and honest they may be. More than anything else, the doctrine of the Restoration sets Mormonism apart from Protestantism.
EDIT: With regard to the question posed in comments, another pillar of Protestant doctrine is known as sola fide, Latin for "only faith." This doctrine takes a very literal reading of Paul's statement that salvation comes by faith as a gift from God and not by works, lest any man should boast (Ephesians 2: 8-9), using it to support the claim that a person's actions, both sinful and virtuous, do not matter to salvation; what matters is accepting Christ and having faith in his atonement.
Latter-Day Saints accept the fide but not the sola, claiming that this is taken out of context, as Jesus (Matthew 7:21), James (James 2: 14-26), and John (Revelation 20: 12-13) all appear to flatly contradict this doctrine, as does modern revelation accepted by Latter-Day Saints as canonical. (See sections 76 and 88 of the Doctrine and Covenants.) Latter-Day Saints do believe that sincere faith is required for salvation, but also that this faith is invalid and useless if it is not what the Book of Mormon terms "faith unto repentance," a faith that motivates a person to actually work to improve and transform their life, to renounce sin and live in a more Christlike manner.