EDIT: stricken text is fixed in Morroblivion v0.61 and later.
A Friend in Deed
The equipment contract can simply be purchased from Relan Tilvur without the need to steal it.
Brandy for the Fundraising Dinner
Dulnea Ralaal gives another bottle of brandy each time she is asked.
Gathering Netch Leather
The Belt of Balyna's Soothing Balm is not actually given to the player as a quest reward, despite the dialog indicating it is given.
Kidnapped by Cultists (maybe a vanilla Morrowind bug?)
Even after rescuing Malexa and reuniting her with Sason, she speaks as though she's still imprisoned ("You don't look like one of those cultists," etc.).
Mysterious Killings in Vivec
The "work" and "woman with dagger" dialog topics don't properly appear with Elam Andas when they should. Also, even when forcing the topics to appear using the console ("addtopic 1womanSwithSaSdagger"), then choosing them and hearing the updated rumors in the Foreign Quarter, the woman still doesn't appear in the Underworks. Again, the console ("setstage fbmwtownvivec 50") must be used to force the quest to complete.
Nels Llendo
After paying/kissing Nels when first meeting him, he does not reappear in the Pelagiad Halfway Tavern (as he did in Morrowind).
Rescue Madura Seran
If the player leaves the hut with Madura (i.e. chooses the "Leave together"/"Follow me" dialog topics) without paying Abassel, Abassel does not get angry or attack: in response to the "Madura Seran" dialog topic, he simply states "She is free to go," whether or not the player had talked with Abassel previously. Also, Madura's "Ald Velothi" dailog topic is bugged, as she states "I'm glad to be back" although still at the camp.
The Silver Staff of Shaming
The Detect Enchantment Ring is not actually given to the player at the start of the quest, despite the dialog indicating it is given. (Maybe this is a problem with implementing Detect Enchantment in Morroblivion? Either way, the dialog is incorrect.)

#1
Fixed.
The topic you should've talked with Elam Andas about is "Work", not "Woman with a dagger". By using console commands you broke the quest yourself.