Chiefly, a failure to coordinate combined arms. When the Scottish and English armies encountered eachother at Falkirk, the English knights charged rather hastily before the rest of the army had gotten into position – but the Scots for some reason had left their archers outside the protection of the schiltrons, so while the knights bounced off the schiltrons to no effect, they overran and wiped out the archers as the Scottish pike and cavalry looked on. Compounding error with error, the Scottish gave King Edward time enough to get his knights back under his command and into formation, and then stupidly charged with their cavalry against Edward’s much larger cavalry and were driven off the field.
*credit to MIke Young
The Scottish schiltrons were left completely undefended, with no cavalry to chase off the English archers and no archers to punish the English cavalry and infantry. Edward was now able to use the same tactics that had been used agaisnt the Welsh at the Battle of Maes Moydog: surrounding his enemy on three sides, he simply had his archers advance and fire into the tightly-packed schiltrons, who couldn’t advance against the archers for fear of leaving themselves open to the knights. Once the schiltrons were weakened enough, Edward sent in the infantry, and the schiltrons broke, and then Edward sent in the cavalry to chase down the fleeing infantry, causing huge casualties.
To use a counter-factual for a moment, imagine that the Scottish archers and cavalry had remained on the inside of the schiltrons – Edward couldn’t have advanced his archers for fear of counter-fire and cavalry charges, reducing their efficacy, and sending in the infantry would have had the same problem. Now, these aren’t unsurmountable obstacles, and at the end of the day Edward had more archers, more cavalry, and more infantry than the Scots, but it would have given the Scots a fighting chance, which they didn’t have in OTL.
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