Ideally, the mezuzah should be affixed with two nails, top and bottom or with double-sided tape strong enough to last for a long time. Scotch tape and mounting putty are not appropriate as they are less permanent.
Even so, your mitzvah was performed according to a minimal standard, and your berachot were not recited in vain. Nevertheless, you should make sure to put them up properly as soon as possible, without a new berachah.
 Shulchan Aruch Y.D. 289:4; Kitzur Shulchan Aruch 11:6; Chayei Adam 15:19.
 Bach 289:7; Shach Y.D. 289:7; Aruch HaShulchan 289:15; Sha’arei Mezuzah 15:18, citing many authorities. Cf. Teshuvos V’Hanhagos 1:646.
 Sha’arei HaMezuzah 15:18:29.
 Agur B’ohalecha (10:6:14) suggests that since scotch tape needs to be torn to be removed, it is still minimally valid. Mounting putty would seem to be minimally valid according to Agur B’ohalecha 10:17:38 and 10:18.