We were talking about this the other day...My notes relate to the renal failure part of the article!!
My take. Nothing is super safe:
morphine metabolized by the liver, and those and a small amount of the parent are renally excreted. Per this article, all are dialyzable. The two glucuronides, M6G (only 10% of metabolism to this) and M3G have opposite effects. M6G is more potent than morphine, and slowly gets in and out of the CNS, so it may be harder to get it out with HD. So, it's OK to use but probably go slow on the dose to be safer (remember the dose of morphine is .1mg/kg, so we probably under-dose our general pain population). 
Hydromorphone - H3G is neuro-excitatory, and can cause bad side effects
Hydrocodone - "slow metabolizers" don't get analgesic effect
Oxycodone - don't use. Both excessive sedation and excitation have been reported
codeine - don't use. Tons of active metabolites that accumulate. 
methadone - not a lot of info, but seems OK, as has a decent fecal excretion. 
fentanyl - not a lot of info but seems OK. metabolized by liver to norfentanyl (inactive)
meperidine - don't use. normeperidine accumulates and it's a bad item!
propoxyphene - I don't like it in general. norpropoxyphene also accumulates and causes adverse effects