Calvin did not like appealing to any tradition or authority other than Scripture. He asserts that the Bible teaches that all have sinned and that all continue to sin, and on that basis each facet of Mariology falls down like dominoes (except perpetual virginity, which he neither defends nor denies based on what he perceives as Scriptural silence). In addition, it is clear that his concerns for a Christocentric soteriology drive him to reject the Roman doctrines regarding Mary. To elevate her to the position they give her would be to deny Christ of his proper place.

Immaculate conception

In his comments on canon 23 of the Council of Trent, Calvin rails against those who say that any person other than Christ is sinless, including Mary:

We condemn those who affirm that a man once justified cannot sin, and likewise those who deny that the truly justified ever fall: those in like manner who assert that a man regenerated by the Spirit of God is able to abstain even from the least sins. These are the delirious dreams of fanatics, who either with devilish arrogance deceive, or with hypocrisy fascinate the minds of men, or plot to lead them to the precipice of despair. As to the special privilege of the Virgin Mary, when they produce the celestial diploma we shall believe what they say: for to what do they here give the name of the Church, but just to the Council of Clermont? Augustine was certainly a member of the Church, and though he in one passage chooses, in order to avoid obloquy, rather to be silent respecting the blessed Virgin, he uniformly, without making her an exception, describes the Whole race of Adam as involved in sin. Nay, he even almost in distinct terms classes her among sinners, when writing to Marcellinus, he says, They err greatly who hold that any of the saints except Christ require not to use this prayer, “Forgive us our debts.” In so doing, they by no means please the saints whom they laud. Chrysostom and Ambrose, who suspect her of having been tempted by ambition, were members of the Church. All these things I mention for no other end but to let my readers understand that there is no figment so nugatory as not to be classed by these blockheads among the Articles of Faith.

Assumption

The only mention of the assumption of Mary that I can find in Calvin's writings implies that he thought the doctrine false. Writing on relics he says:

The belief that the body of the Virgin was not interred on earth, but was taken to heaven, has deprived them of all pretext for manufacturing any relics of her remains, which otherwise might have been sufficiently abundant to fill a whole churchyard.

Perpetual virginity

Calvin denies that Mary's words in Luke 1:34 necessitate a vow of virginity, but doesn't thereby take a firm stance one way or the other on her perpetual virginity:

The conjecture which some have drawn from these words, that she had formed a vow of perpetual virginity, is unfounded and altogether absurd. She would, in that case, have committed treachery by allowing herself to be united to a husband, and would have poured contempt on the holy covenant of marriage; which could not have been done without mockery of God. Although the Papists have exercised barbarous tyranny on this subject, yet they have never proceeded so far as to allow the wife to form a vow of continence at her own pleasure.

In his commentary on Matthew 1:25 he stakes out a firmly agnostic position on the doctrine:

It is said that Joseph knew her not till she had brought forth her first-born son: but this is limited to that very time. What took place afterwards, the historian does not inform us. Such is well known to have been the practice of the inspired writers. Certainly, no man will ever raise a question on this subject, except from curiosity; and no man will obstinately keep up the argument, except from an extreme fondness for disputation.

Intercessory role

In his commentary on John 2:4, he says that Mary did wrong by telling Christ what to do:

Though she was not moved by ambition, nor by any carnal affection, still she did wrong in going beyond her proper bounds. ... Christ, therefore, addresses his mother in this manner, in order to lay down a perpetual and general instruction to all ages, that his divine glory must not be obscured by excessive honor paid to his mother.

In his 1544 satirical attack on the Catholic faculty in Paris, he rejects the necessity and propriety of praying to Mary:

To flee to the Virgin, passing by Christ, and in prayer to address her instead of God, who sees not to be a profane practice? It is assuredly altogether alien from the Word of God. ... What access have we to the Virgin, for the purpose of holding conference with her? Besides, why use the salutation at the time when they implore the influence of the Spirit, unless to pervert it into a form of prayer?