PBA: I dunno. I’ve seen leases with the clause that as long as there is 24-hour notice, he can show the apartment during any daytime hours during the final month/2 months of the lease. Hopefully he’ll respect your wishes re Shabbos/the birthday party, but depending on the lease it could very well be his right.
Joseph: Again, depending on the lease, he has whatever rights. And just because it’s not worth it for him to sue you doesn’t make it right and/or Muttar to lie and pretend to have “personal issues” or whatever to avoid showing.