In general, there is no issue with leaving a browser open. However, if using a number of browser extensions or plugins, these can cause memory leaks which use up your resources until you close the browser. These leaks are invariably caused by programming issues.
I've had situations where Firefox was using around 400MB of memory, then come back hours later to discover it utilizing over 1GB of memory.
Mozilla has taken steps with extensions or plugins to reduce this issue, but still exists. And not limited to Firefox by any means.