Yes. Have you heard the true story about the conscientious homeowner from Regina who lived in a pre-Second World War bungalow? One summer he insulated his attic, with proper ventilation and all and the following winter his heating bills went up, not down. The next summer he insulated the walls on the outside -- and the following winter his heating bills went up again!
The gentleman in Regina lived in a balloon-framed house. The hollow walls opened right up into the attic. When he insulated the attic he effectively lost less energy through the ceiling, but by adding ventilation to a roof that had previously been sealed shut, he created a path for the heat to flow through the hollow walls, up past the insulation in the attic and out the ventilator. When he insulated the outside of the walls, he made the inside of the walls hotter still and they pumped air and heat out the top of the house even faster. Sealing off the top of the open walls brought things back into line -- finally!
The Ecology House in Toronto transformed a large brick wall in the building into a thermal mass wall, designed to heat the house with passive solar energy. But it didn't work. There was an air space between the double brick wall and it was sneaking all the heat right up through the attic.
Air spaces that open into the attic or that allow convection currents between the insulation and the warm side of the house can partially or totally negate the energy-saving effects of thermal insulation. Here are some common examples:
-- Old insulation practices that purposefully left an air space between the insulation and the outside sheathing can negate further exterior insulation. If the space is fairly large, and particularly if it may cause condensation problems, it may be economical to inject loose fill insulation into the cavity from the outside before adding exterior insulation. The loose fill won't add much thermal resistance to the wall, but it will protect the other insulation you are going to add to the outside. You don't have to patch the holes carefully as the insulation and siding will cover them.
-- When 150 mm (6 in.) fiberglass batts are shoved into the wall, they often leave triangular air spaces in the corners. There is not much you can do about it once the wall is covered, just don't be guilty of doing it yourself and ensure that anyone working for you pushes them all the way to the sheathing and pulls the face back up flush.
-- Balloon-frame walls are good candidates for loose-fill insulation poured in from the attic; cap the hole afterwards. This is an easy job for do-it-yourselfers.
-- See more examples in the database: INSULATING THE OUTSIDE OF WALLS.