The Mishna gives a list of bad wicks and oils, and the gemara explains that the problem with them is that they flicker and don't burn well. However, the gemara doesn't say why this is so problematic. There seem to be 3 approaches. Rashi writes that there is a concern that you will adjust the candle to make the flame burn better, thereby violating Shabbos. The Rambam (pirush hamishna) writes that if the flame flickers, one is likely to leave the room thereby undermining the entire purpose of lighting candles for shabbos [However, in Hil. Shabbos (5:8) he concurs with Rashi]. The Rambam's approach is to equate the bad burning oils with the bad smelling oils where the gemara says explicitly that the concern is that you will leave the room. There is a third approach cited in the Tosafos Yeshanim (printed in the vilna edition, bottom right margin) that is similar to the Rambam who say that the concern is that the flame will actually extinguish and will undermine the entire purpose of the candles which are to allow for shalom bayis.
The approach of the Tosafos Yeshanim is similar to that of the Rambam, and even helps avoid the Rashash's question. The Rashash asks on the approach of the Rambam, why would someone leave a room with poor lighting and prefer a dark room with on light? According to the Tosafos Yeshanim the concern is that the candle will go out completely and undermine its purpose. The main distinction between the approach of Rashi and that of the Rambam and Tosafos Yeshanim is that Rashi's problem applies to all the candles in the home, whereas the issue of the Rambam and Tosafos Yeshanim only applies to the candle with which the mitzvah was performed.
In the context of Chanuka, Tosafos asks on the opinion who says that one cannot use bad wick and oils on shabbos chanuka because one is allowed to use the light and may come to adjust it. Why not say that just as one can't use bad wick and oils for chanuka candles during the week because of כבתה זקוק לה, one must relight if it goes out, for that same reason it can't be used on Shabbos? The Rashash points out that Rashi seems to answer this question by adding the words - דלמא פשע ולא מתקן לה. Meaning, we aren't concerned for the candles going out on Friday night because since it is prohibited to relight it, the person is considered an a'nus and is not in violation of anything. Rather, the concern is that he will be neglectful and not relight the candles when he is able to. This reason only applies during the week, compelling the gemara to resort to another rationale on shabbos, namely - מותר להשתמש לאורה and therefore there is a concern of adjusting the light.
Rashi's approach answers a much more fundamental question. The implication is that when chazal forbid the use of bad wicks and oils, they even forbid their use when there is no alternative. In the context of Shabbos where the concern is adjusting the flame and violating Shabbos, it makes sense for chazal to say that it's better to skip the mitzvah altogether, than to light candles in a way that may lead you to violate shabbos. But, in the context of Chanuka, if one has not better wick an oils, does it make sense to tell him to not light at all out of a concern of them going out? Wouldn't it be better to light the bad wicks and oils based on the chance that they will stay lit and he will fulfill the mitzvah? According to Rashi this question can be answered. Had Chazal permitted the use of the bad wicks and oils, it could lead to a situation where the person is neglectful and fails to relight when he should have. Therefore, they forbade the use of these wicks and oils creating a situation of o'nes, so that if he has nothing else he is an a'nus in not fulfilling the mitzvah.
A similar question can be asked on the Rambam and Tosafos Yeshanim back in the context of shabbos candles. Why would we say to someone who only has bad wicks and oils that he should not light at all? Wouldn't it be better to light and allow for the possibility of fulfilling the mitzvah, rather than not light at all and definitely not fulfilling the mitzvah? According to rashi who is concerned for the violation of shabbos - שמא יטה, the chance of the mitzvah isn't worth the risk of violating shabbos, but according to the Rambam and T.Y. where the concern is merely not fulfilling the mitzvah, it is better to use the bad wicks an oils rather than use nothing!? Perhaps they understand that the entire mishna is speaking when one has an alternative to light with proper wicks and oils, but in the absence of an alternative, something is still better than nothing.