Is it okay to substitute 1A 40V Schottky with 40V 3A version of it and what can go wrong with that setup?
They have nearly the same VF and Rth-JA at the same conditions. But 5822 has higher leakage current level.
So the answer is: It depends on usage and required electrical performance.
If the diode is a part of an SMPS (e.g. buck converter), or it's used to protect semiconductors against spikes (e.g. placing across the coil of a relay), or simply it's used just for a reverse polarity protection purpose then yes, you can safely use 5822 in place of a 5819.
But if it's used in a power-OR of a circuit including backup battery then the leakage current may be a problem.
The size should be considered as well since 5822 is bigger. It also requires bigger holes (1.5mm dia) for proper mounting and soldering.