Paint:
These come as water-based (eg Latex) and petroleum hydrocarbon-based (eg oil paints, enamels). Water-based latex paints are generally considered safe around birds although the fumes may cause some eye irritation. Birds should not be exposed to the vapours of hydrocarbon-based paints. However, once the paint has dried and the vapours have dissipated, there is no problem for birds.
Carpets:
New carpets and underlay may liberate toxic fumes.
Cupboards, Shelving, etc:
These may be made of materials (eg particle board) that are made up with adhesives that may contain toxic additives (eg formaldehyde).
In order to dissipate vapours from new carpets, cupboards etc, one should turn the heat up to maximum and keep the birds off the premises for a minimum of two weeks. Ensure adequate ventilation prior to bringing the birds into the new home after the above measures have been carried out.