1:
Our mishnah continues where the previous mishnah left off. This is typical of the associative thought processes of the mishnah - and of the Gemara. The discussion in Mishnah Five concerning bridegroom's reading the Shema brought up the idiosyncratic behaviour of Rabban Gamli'el in this regard. Having mentioned the irregular customs of that sage in one area, the next two mishnayot discuss some more of his idiosyncrasies. Only in Mishnah Eight will the subject of bridegrooms and the Recitation of the Shema be restored. (In the Gemara all these mishnayot are treated as one mishnah - not without some logical justification.)
2:
Our mishnah is based on the laws of mourning. Our sources are not unanimous whether the duty to sit shiv'ah [to observe seven days intensive mourning on the decease of immediate relatives] is de-orayta [derived from the Written Torah] or mi-de-rabbanan [a rabbinic institution]. A third view - which seems to be the assumption of the Tanna in our mishnah - is that the duty of mourning for one day is de-orayta and for the other six days it is mi-de-rabbanan.
3:
Mourning for one's spouse, parent, sibling and offspring is a religious duty: it and its regulations should be observed even when not prompted by natural affection and emotion. The following acts are prohibited to someone in statutory mourning: cutting the hair, wearing newly-washed clothes, bathing, sexual intercourse, wearing shoes, going to work, studying Torah, offering greetings (and three other acts which are no longer part of our life-style). All the prohibited actions are considered to be actions that bring pleasure and/or ease, and therefore not compatible with the mourner's situation. Where it is necessary to perform any of these actions for reasons not connected with pleasure or ease the restriction may be eased.
4:
Let us illustrate with the instance of our mishnah. Simple washing of hands and face is not prohibited; if one has become covered in dirt or sweat bathing is not prohibited - and so forth. Rabban Gamli'el, in our mishnah, adds a further exemption (which is accepted into halakhah): where not bathing (for instance) would cause real suffering (mental or physical) the prohibition is to be waived - even if that suffering derives from one's having been "pampered", as he readily admits.