It depends on your end application and the components of the buffer on which the PCR product is stored (i.e. is it an unpurified reaction? etc). For most purposes leaving a PCR product inadvertently on the bench overnight has no consequences, but it's better to keep molecular biology reagents and products on ice or frozen just to play it safe
If you are, however, designing a specific procedure where PCR products will have to sit at room temperature during a certain period, it is hard to provide precise answers. You have to validate the procedure and find out by yourself whether leaving the products at RT influences or not the result of the assay you have in mind.
It depends on your end application and the components of the buffer on which the PCR product is stored (i.e. is it an unpurified reaction? etc). For most purposes leaving a PCR product inadvertently on the bench overnight has no consequences, but it's better to keep molecular biology reagents and products on ice or frozen just to play it safe
If you are, however, designing a specific procedure where PCR products will have to sit at room temperature during a certain period, it is hard to provide precise answers. You have to validate the procedure and find out by yourself whether leaving the products at RT influences or not the result of the assay you have in mind.
As a general rule, DNA is stable at room temperature which is not the case for RNA. A PCR product can be left at room temperature without risk, but for long term storage it is better to store frozen.
If it is a purified product, free of enzymes etc., then it should be quite stable as long as it is protected from light. UV is a real killer and should be avoided in gel purifications etc if at all possible.