Tosfos (69a kol hanilkat) discusses how the part of the vineyard that grew after the Tznuim’s declaration did not prohibit the rest of the vine. Tosfos assumes that the regular rules of bittul – nullification of a prohibition in a larger mixture – would not apply, since the fourth year vineyard is a davar sheyesh lo matirin – a prohibition which will become permitted. See the Rama YD 102:4 for a conflicting opinion.
Cuthean produce vs. D’mai
There is a dispute among the Tannaim whether Cutheans are Halachically Jewish, but just less trustworthy, or not Jewish at all. This depends on whether we classify them as Geirei Arayos – converts only due to fear of lions – or Geirei Emes – true converts. (See Tosfos Chulin on how to reconcile the second opinion with the verses in Melachim that state the history of the Cutheans). The Rishonim explain that the author of the braisa in our Gemora holds that the Cutheans are Jews, but just not trustworthy. Their produce is still different than D’mai, the produce of Amei Haaretz, on which there is a doubt as to some of the tithes. D’mai is most likely tithed, but the Sages instituted an assumption of some tithes not taken. Since it’s a special stringency, there are areas where the Sages allowed leniency (e.g., poor people can eat it, it can be separated on twilight Friday night). However, the produce of the Cutheans are considered definitely not tithed, and these leniencies do not apply.
Ye’ush vs. Hefker
The Rishonim question why a person should have to declare the extra fallen sheaves to be hefker for the poor people. Presumably, the owners – who are ready to declare hefker on these sheaves – have given up on them, and such despair (ye’ush) is sufficient for someone to take ownership. Even those opinions earlier in the perek who do not accept ye’ush to transfer ownership, will agree that changing possession together with ye’ush will. Tosfos (69a kol shelaktu) answers that ye’ush will effectuate ownership, but not remove the need for tithes. Tithes are not necessary for hefker, since the Torah states that tithes should be given to the Levi “ki ein lo chelek v’nachala imach” – because he does not have a portion and inheritance with you. This implies that hefker, where the Levi has equal rights with you and everyone else, will not require tithes. Ye’ush, however, will only transfer the grain to the poor, but not give the Levi (or anyone else) rights to the sheaves. In addition, Tosfos states that the ye’ush here is only vis a vis the poor people, and is no better than hefker only to the poor, which is not considered hefker at all.