In the US, even if you are a registered Organ Donor, a family member must still sign a document stating which organs may be removed at your time of death.
The only bad thing I have seen in this process is that sometimes the people responsible for gaining this permission put a little pressure on the family members at a time of grief.
WTF are you gonna do with your organs after you are dead anyway? Give them to your grandchildren?
If you want an open casket funeral nothing will be noticable that your Organs have been removed.