This was such a problem that it's now just a normal setting in the Video settings. Just go into the options menu into Video settings and change "Texture Fade" to Off and high res textures will be loaded the first time, for no fade in.
The method below works but it's more of a "hack" than just using the in-game option. It used to be the only way to change it.
If you’ve noticed texture pop-up when you open loot containers and it’s irritating you, you can greatly reduce it or eliminate it with this using a trick found How to Improve Borderlands 2 with .ini File Tweaks.
Find the file located at
C:\Users\%USERNAME%\Documents\My Games\Borderlands 2\WillowGame\Config\WillowEngine.ini. You can edit this file safely with any text editor (notepad).
As Gamefront notes, you can change the following set of settings (ctrl F to find them)
To all zeros, like so:
If you're scared you can make a backup copy of your text file, but the above are the defaults (not the zeros) so you can set them back or play with them as you like. If you notice a significant performance drop (I certainly haven't) you can restore the settings.
The link has some other tweaks that may improve aesthetics or performance for the more picky. But this issue bugs the most people I know of.