Michael Welter:
This past weekend at Mass, our priest said that we don’t do intinction anymore because there is an increase chance of dripping some of the Precious Blood on the floor.
Not if a communion-plate is used under the chin, and if the Host is intincted by the priest and placed directly on the tongue of the communicant. From
Redemptionis Sacramentum:
[93.] The Communion-plate for the Communion of the faithful should be retained, so as to avoid the danger of the sacred host or some fragment of it falling.180
And, about intinction from RS:
[103.] The norms of the Roman Missal admit the principle that in cases where Communion is administered under both kinds, “the Blood of the Lord may be received either by drinking from the chalice directly, or by intinction, or by means of a tube or a spoon”.191 As regards the administering of Communion to lay members of Christ’s faithful, the Bishops may exclude Communion with the tube or the spoon where this is not the local custom, though the option of administering Communion by intinction always remains. **If this modality is employed, however, hosts should be used which are neither too thin nor too small, and the communicant should receive the Sacrament from the Priest only on the tongue.**192
[104.] The communicant must not be permitted to intinct the host himself in the chalice, nor to receive the intincted host in the hand. As for the host to be used for the intinction, it should be made of valid matter, also consecrated; it is altogether forbidden to use non-consecrated bread or other matter.
Read through the entire document if you have any further concerns about liturgical abuses. Consider printing it out and discussing this with your priest.
adoremus.org/RedemptionisSacramentum.html