In these two subsections of his essay on yichud, Rav Waldenberg focuses on the heter of בעלה בעיר, that there is no prohibition of yichud for a woman so long as her husband is present in the city.
In subsection four, his main concern is to assert the fact that there is indeed no prohibition of yichud under such circumstances - not only is there no punishment, but there is actually nothing prohibited about a woman being alone with a man so long as her husband is local.
In the section subsection, Rav Waldenberg pushes the limits of this leniency. What if a husband is in the city, but the woman is alone with a man somewhere other than her own house? If the leniency is based on the fact that the woman fears that her husband might come home at any moment and therefore she will not do anything illicit with the other man, then it would seem that this fear is absent in such a case and perhaps the leniency does not apply! This is in fact the view of the Chochmat Adam (among others).
However, Rav Waldenberg retorts that when Rambam mentions the idea of בעלה בעיר, he does not say that she fears her husband's return, but simply that she has a fear (more reverence than dread) of her husband. As such, one could posit that the mere presence of her husband in the city will serve as a restraining force on the woman even if she is not at home and her husband is unaware of her precise location. This view is put forward by the Sefer Yedei Eliyahu.
However, that position is then attacked from two sides. The Kol Eliyahu takes the predictable approach, reverting to our earlier statement that as long as the husband does not know where the woman is, her fear of him will be diminished and thus there should be a prohibition of yichud. The Chida comes from the opposite direction and says that since the Gemara simply says that we are lenient when the husband is in the city, it is not up to us to make distinctions within the details and thus there should be no prohibition in such a case. However, the Sefer Nishmat Kol Chai (Rav Chaim Palagi) retorts that since this leniency in the Gemara is stated with a reason for the leniency, that opens up room for us to make distinctions when warranted.
The Nishmat Kol Chai cites a position of the Radbaz that a woman can be in a yichud situation outside of her home so long as her husband in the city if that other location is a place of employment. In fact, this logic is the basis of allowing women to work in situations where they may encounter situations of yichud. While this would seem to support the lenient position stated above, in fact Rav Palagi claims that it works the other way - the only reason that such an arrangement is allowed is because the husband is aware of where the woman is and may even have occasion to show up at her place of employment during the day. However, if she were to be in an undisclosed location with another man, he would rule that to be forbidden. Rav Palagi concludes by stating that everyone agrees that yichud outside of the home would be forbidden.
Rav Waldenberg takes issue with Rav Palagi on two counts. First, he notes that it is not universally agreed that there is a prohibition in this situation. Second, with regard to the distinction of the Radbaz, he notes that perhaps when a woman is in a yichud situation with the permission of her husband she is more likely to do something inappropriate, since she assumes that since her husband is aware of where she is and approves of it, that she therefore does not worry that he will ever make an appearance. Ultimately, Rav Waldenberg that this issue seems to be stuck in a debate among the Gedolei Acharonim.
However, Rav Waldenberg goes even further than the Chochmat Adam. The Chochmat Adam writes that if the husband gives his wife permission to speak in private with another man, it would be forbidden for them to close the door. Rav Waldenberg claims that in such a situation that would actually increase the chances that the husband would show up to check things out, and thus perhaps there is still no prohibition of yichud under the rubric of בעלה בעיר. He cites the Dovev Meisharim who rules similarly, at least when livelihood is at stake.
The end of the teshuva raises as a possible point of proof a case of whether or not there is yichud in a succah, specifically with regard to having a chupah be there. Ultimately, Rav Waldenberg discounts such a case as having any bearing on our case since a new bride may not yet have a fully established fear of her husband, and thus the concept of בעלה בעיר might not be in full effect.