For instance, if the daily, or even the 5-minute gave you a solid "signal" but the higher time frames did not, would you forego the trade?
No, of course not, because I am not trading "siganls" in the sens of "MA1 crossed MA2 go long." I am trading price and I am looking at support and resistance, prior highs and prior lows. Most of my trades take place at one extreme or the other of a defined range or channel. I like to be the guy taking the other side of the stop losses that get triggered when price probes a level. Now, if I know price is near the top of a daily trend channel, then I will perhaps be more quick to pull the trigger on a short when price is trading at that level and I see indications that the market is not willing to bid any higher.