Excellent question, and one I've personally struggled with for some time.
I'd like to offer two very different answers that aren't necessarily congruent, if you'll permit me.
The first is the orthodox Lutheran answer. Confessional Lutheranism is insistent that there is an absolute difference between the revealed God and the hidden God. God revealed is God in his grace, mercy, and forgiveness known through his promises and acts of redemptive in history and the scriptures. God hidden is God sought out on human initiative through intellectual inquiry who can only be known in his wrath and condemnation. Therefore, any knowledge of God that comes apart from the scriptures can only ultimately lead to a knowledge of God that provides no balm for guilty consciences.
Ok, now that that's out of the way to satisfy my fellow Lutherans... I think Eucharistic and Marian apparitions within the Catholic Church are entirely valid, because the Eucharist is Christ on earth and Mary is actively interceding for her Son's body, the church, and we should expect nothing less.
Wait, what?
Oh, yes. As a Lutheran, I firmly believe that the Eucharist is Christ's body and blood, and if Christ chooses to reveal the hidden reality of his physical presence in the sight of his faithful, that is his prerogative. And as an evangelical catholic (another and more accurate term for Lutheran), I absolutely believe that Queen Mary is in heaven attending her Son, and if he wishes to use her to further his mission to redeem the world by making her concern for his faithful known, then that too is his prerogative. I'm perfectly comfortable with both.
Do I think every instance of Marian and Eucharistic apparitions are valid? No, of course not, and I doubt that every instance are considered valid among Catholics. But many surely are, and that causes me no trouble either as a Lutheran nor as an evangelical catholic.