On my Pi B+, and B model 2 there is a piece of orange see-through tape stuck across the top of the HDMI connector.
What is the purpose of this piece of tape? And are there any damaging effects if I remove it?
I believe the tape is useful for manufacturing using a vacuum based pick and place machine. The machine can't pick the parts up if they're full of holes. Removing it shouldn't do any harm.
Due to its large range of temperature stability, and its electrical isolation ability, Kapton tape is usually used in electronic manufacturing as an insulation and protection layer on electrostatic sensitive and fragile components. As it can sustain the temperature needed for a reflow soldering operation, its protection is available throughout the whole production process, and Kapton is often still present in the final consumer product.
The Kapton tape was used to protect the HDMI connector when it entered the reflow soldering bath. Removing the tape has no negative consequences. Quite to the contrary, Kapton tape is known to become brittle after a while in humid (Earth-like) environments. One does not want those pieces of Kapton tape to enter any cooling fan when one is using one of those.