Dangers from intermittent phase issues
You may not have trouble with your appliances, but the intermittent connection could be generating an enormous amount of heat and spark an electrical fire. If the intermittent connection is on the utility pole then you probably don't need to feel responsible; if it's in your breaker box or in your wall then you should be extremely concerned.

As a rule of thumb, a loose connection where your lights are either completely on or completely off isn't a concern; it's the times when your lights are half on where that connection can be dissipating an enormous amount of energy. Worst case, the connection could be dissipating on the order of one quarter of the full usual load, so with a 3400W electric dryer you could have almost a kilowatt of power heating up that connection. Could get entertaining fast.