As it appears, my Thunderbolt/mini DisplayPort port on my MBP mid-2012 is nonfunctional, so I cannot use my DP-VGA adapter anymore to connect to external monitors/projectors.
What alternatives are there and what are the limitations?
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You can use a USB Display Adapter. One like this could work.
Some display adapters only support digital formats (HDMI, DVI-D...) so if your projector only supports analog signals (i.e. VGA) then make sure the adapter you get supports it.
One limitation of USB display adapters is their limited bandwidth, and therefore limited resolution. For a projector, there shouldn't be any issues, but if you wanted to power a 4k monitor, they may not work. Again, check the specs on the display adapter you are looking for and make sure it supports your desired resolution.