It shouldn't be a problem! I believe it's probably a fungal issue so make sure the fronds do not get too much water on them (only water the base and make sure the sprinklers aren't getting the fronds wet). If it's a healthy palm, it will grow out of it without an issue, but palms that aren't healthy can be further set back with leaf spotting.
I had this happen on my windmill palm when it was younger (much more severe than the damage on yours) and it completely grew out of it without any problem. It just looked bad for a year because there were leaf spots on just about every frond.
-Alex