The Yu Yu Hakusho anime is missing a lot of scenes from Yoshihiro Togashi's original manga. The scenes in question may not be integral to the overarching plot, but they do add something to the audience's experience of the series. Some of these moments provide noteworthy details that contextualize the story and the characters in it. One such moment features Urameshi Yusuke's father.
In the anime, Yusuke's father is not seen at all. This might have to do with his minimal influence in the story. He only shows up for one chapter near the end of the manga. Even Yusuke's ancestral forefather Raizen gets more to do than this mystery man. However, learning more about Yusuke's father could still be a good way to understand the Urameshi family a little better.
Yusuke's father only shows up in Chapter 173 of the manga, "Harmonious Soldier." This chapter is an anthology that covers minor events among the cast. The only vignette to make it into the anime is a training session between Chu and Natsume, neither of whom have anything to do with Yusuke's father. This chapter is largely inconsequential to the overarching plot, which is probably why it was mostly omitted.
The vignette featuring Yusuke's father is titled "The Once-a-Month Marriage." This title alone suggests a few things. The most obvious is that Yusuke's parents live separately; this much can at least be inferred from the anime. It also suggests that while living together didn't work out, they still find enough pleasure in each other's company to regularly meet up. Whatever the cause of their breakup, it seems that they left each other on relatively good terms.
Yusuke's father isn't exactly allowed back into the Urameshi family home, but he's willing to leave his own doors open to an opportunity to help out. As he and Yusuke's mother Atsuko observed the boy from afar, he noted how their son was enjoying himself. He also asked if they needed any financial support -- something he's apparently asked before, only to be rebuffed by Atsuko. He also suggested that the two of them get back together, but Atsuko was sure they'd just fight and split up again. It's clear from the vignette that Yusuke's father still cares about his old family.
It's suggested that Yusuke's father's feelings for his family aren't exactly mutual. Besides Atsuko's unwillingness to get back together with him, Yusuke would probably attack the man for spanking him when he was a toddler. It certainly doesn't help that Yusuke has the strength of an S-Rank demon. Yusuke's father saw this as a form of tough love, although Atsuko seems to believe that Yusuke would beg to differ.
Beyond his former family, Yusuke's father has a shoddy love life. He's apparently been in several relationships since leaving Atsuko. His inability to stay in a proper relationship with one woman may further explain why he and Atsuko split up.
What's funny is how Atsuko still acts somewhat warmly toward Yusuke's father despite their current status. She even offered to spend the whole night with him when she realized he got dumped again. Whether this kind of relationship is healthy is debatable, but there are certainly worse fates for exes.
It's probably for the best that Yusuke's father never made a proper appearance in the anime. He doesn't add a lot to the story and Yusuke remains a well-developed character without him. Even the manga treats the man as an afterthought, as he only appears within the twilight chapters after everything else has been wrapped up. Regardless, it's interesting to have this brief glimpse into Yusuke's family life, and it was nice of Togashi to introduce readers to him, even if only briefly.
