Question: Can one use a disposable cup for Kiddush?
Answer: The Shulchan Aruch (OC 183:3) writes that one mustn’t use a cracked cup for bentching. The Magen Avraham (OC 183:5) writes that even a broken base disqualifies the cup. The Mishna Berura (183:11) applies this halacha to the cup used for kiddush and havdala, too (See Shulchan Aruch OC 271:10).
There is a machlokes as to how to apply this halacha to disposable cups.
R’ Moshe Feinstein (Igros Moshe OC 2:75; 3:39) writes that one mustn’t use a disposable cup for kiddush as it isn’t respectable. Using a disposable cup would be worse than a real cup with a cracked base. R’ Yitzchak Yaakov Weiss (Minchas Yitzchak 10:23) adds that just as one wouldn’t tovel such a cup as it isn’t considered a proper kli, so too it doesn’t qualify as a proper kli for kiddush (See Ohr Letzion 2:47:12).
R’ Binyamin Zilber (Az Nidberu 6:48), however, writes that there is no need for the cup to be particularly respectable. If there is no nicer cup available, one may use a disposable one. Similarly, R’ Eliezer Waldenberg (Tzitz Eliezer 12:23) writes that people often reuse disposable cups, especially those made for hot drinks. Thus, irrespective as to whether one ever reuses them or not, they are considered to be proper cups and may be used for kiddush (See Beer Moshe 5:55; Rivevos Ephraim 1:150:2).
R’ Shlomo Zalman Auerbach (quoted in Shemiras Shabbos Kehilchasa 47:n51) allows one to use disposable cups that are respectable looking and would not look out of place at a dinner.In conclusion, one should try to use a proper cup where possible, though when necessary, one can use a disposable cup.