What is the most effective way of reducing blunders? Many people suggest tactical exercises as the best form of study for this purpose but I find that it only attacks the problem from one dimension (not making the strongest in a position). Analyzing my own games I find that I'm much more likely to lose a game by making a dumb blunder rather than missing a winning combination, so solving more chess puzzles doesn't seem very effective at improving that. Any other forms of exercise that could help with this?
If you want to avoid "dumb blunders" - i.e. just dropping a piece you've left hanging on the other side of the board - a simple method is to take an inventory of the position before you do anything else on each move. Checking which of your pieces are attacked and which of your pieces are hanging would be a good start. The brain will catalogue this information into 8x8-grid punch-card type patterns in your head that act as a warning system against stupid errors.

It can however be surprisingly difficult to take a regimented approach like this even if on the surface it seems quite a trivial task to complete at the start of each of your moves. The brain has a tendency to immediately want to investigate interesting lines and will wander sometimes never to return. Even harder if you're an older player who has never applied such discipline.

But if you stick at it over time it becomes second nature and you just see better and don't blunder as much.