It Doesn’t Take Much
במדבר יט,ב: וְיִקְחּו אֵּלֶיָך פָּרָּה אֲדֻּמָּה תְמִ ימָּה אֲשֶר אֵּין־בָּּה מּום אֲשֶר לֹא־עָּלָּה עָּלֶיהָּ עֹל
Baal HaTurim notes that the word על is missing the letter Vav. This teaches that the Red Cow did not need to have drawn the yoke, in order to be rendered invalid. It is sufficient for the yoke just to have been placed on its back to become disqualified.
Like the Mother
Baal HaTurim points out that the numerical value of פרה אדומה (341) is the equivalent of זה על עון עגל (this for the sin of the Calf). Chazal have taught us that the Parah Adumah came to atone for the sin of the Golden Calf - 'Let the mother come and wipe up the mess that her baby made'.
The Fig-Tree and the Vine
Baal HaTurim observes that the Torah usually precedes the vine to the fig-tree. The only time it does not do so is here (20:5). The reason for this is because it follows the Parshah of the Parah Adumah, and for the burning of the Parah Adumah they would use wood from a fig-tree.
Some Brother
Moshe sent messengers to the King of Edom saying "Please let us pass". But when he sent messengers to Sichon, he failed to say please. Baal HaTurim explains that with regard to Eisav, he was talking to Yisrael's brother, and his desire for peace was a genuine one.