Are there any problems with leaving my Raspberry Pi powered even though it is shutdown?
Sometimes I forget to unplug it after running
sudo halt, so I was wondering if I was affecting the lifespan of my Raspberry Pi or something like that.
Yes, every electronics degrades while it ages, if connected on some power source. The "problem" lies in electronic characteristics itself. One of the phenomena is called electromigration, where IC (actually whole PCB) degrades under various "nonideal" (i.e. working) conditions: current, time, temperature (which is also consequently caused by resistance properties, when device/IC is attached to power source), etc.
But... those degradations will probably not be felt for the time of your life.
What can be critical is flash memory in SD card. Every read/write cycle will slightly kill cells and you can't do nothing about it. Regarding the endurance (Sandisk SD specs, 1.8):
SanDisk SD cards have an endurance specification for each sector of 100,000 writes typical (reading a logical sector is unlimited). This far exceeds what is typically required in almost all SD Card applications. Therefore, extremely heavy use of the card in cellular phones, personal communicators, pagers and voice recorders will use only a fraction of the total endurance over the device’s lifetime. For instance—it would take over 10 years to wear out an area on an SD Card based on a file of any size (from 512 bytes to maximum capacity) being rewritten 3 times per hour, 8 hours a day, 365 days per year. With typical applications, the endurance limit is not of any practical concern to the vast majority of users.
sudo shutdown the system, the SD will unmount and no I/O activity will be on the SDI line (at least in theory).
You WILL NOT feel any degradations regarding Raspberry Pi hardware characteristics over time if it stay plugged into power source (of course, we assume that everything else, e.g. power source stability, room temerature, etc. stays in normal conditions).