I'm a dual US/German citizen, residing in the UK. I am currently applying for a visa for South Africa with my German passport, which may take another 3 weeks to process. Now, I need to travel to the US for a month. I am still in possession of my US passport so will obviously use that passport when I enter the US. I have authorized a friend to pick up my German passport and send it to me in the US, once the South African embassy is done processing my visa application. My worry is that since I entered the UK using my German passport, it may cause problems if I leave on a different passport. So my question is, do I need to show a passport at the UK border before I leave?
Largely No, but...
The UK does not have exit immigration checks. Your passport will be checked by airlines or ferry staff to verify you'll be accepted into your destination, but no-one from the UK Border Agency will see/check/etc you or your passport
However... The UK is slowly, and many would say somewhat incompetently, rolling out a scheme originally called E-Borders. That will involve carriers (ferries, trains, airlines etc) sending electronically to the UKBA the details of everyone entering and leaving the UK. It was partly deployed, and I believe will be rolled into the new program. Under that, there's a chance that the UKBA will be told the details of you leaving.
Your problem is more likely to be on your return to the UK. You'd be entering the UK on your US passport, which only entitles you to a short visit (up to 90 days), and not for the purposes of living in the UK. You'll get a stamp. You may have issues with convincing them to let you in given that you do live in the UK, and you may have issues if you don't leave the UK within 90 days on the US passport as the system may detect you as an overstay.