I accidentally put a shut off valve in the wrong direction of the water flow (according to the little arrow). It will be in the closed position most of the time because it is re-directing water to a filter bypass.

Does it matter?

If the valve has an arrow on it, then it does matter. If it is a gate or globe valve, you in the OFF position, you have pressure on the wrong side of the gate or washer. In a typical residential system, the issue is more philosophical than a real issue.

If it's a stop and waste type valve with a small cap that unscrews, (see image below), it
really shouldn't matter as long as it shuts the water where you need it to and lets the water flow when opened.

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This slow drip will waste 7+ gallons of water per day.

If it has an arrow on it, then it almost has to be a globe/stop valve, in which case it is really the wrong valve anyway. Other than that there is only a slight degradation by installing it backwards. The big advantage of having it in the correct direction is that by turning it off and relieving the pressure, you can repack it without turning off the entire water system.

it will shut the water but the flow should always come from under the seat. the valve can be shut and the packing nut removed so the valve can be repacked but only if installed in the right orientation.
even if there is no arrow, simply look in the ends to make sure the pressure comes from below the seat. (boston navy yard training)

Author: amhplumb (PA)
If the valve is a stop and waste type, that being it having a small drain on it, as another plumber pointed out, the valve will indeed turn the water on and off and you won't have any noticeable difference in the valve's operation if installed in the wrong flow direction. You will retain the stop & waste valve's "stop" function. However, you will lose the valve's "waste" capabilities. Installed backwards, the drain port will remain charged, regardless of whether or not the valve is in the closed position. If the valve serves something such as a hose bib that has to be winterized, being able to utilize the drain after the valve has been turned off is very critical in being able to drain the piping. But, if you are using the valve on something that doesn't require the drain, you should be okay. Next time, check the arrow! If no arrow, the flow should go against the washer side of the stem. Or, the pressure side should not be on the side of the stem.