I will answer your questions since I run an unlocking service and am very knowledgeable on the subject.
Does unlocking the phone while still being on the network cause any "errors" on said network (e.g. Unlocking AT&T and staying on AT&T)?
No it causes no problems at all. The phone never sends a signal to any network that is is subsidy locked or unlocked.
Does the unlocked phone need anything when taking it to another network (e.g. Unlocked AT&T android phone and going to straighttalk)?
Yes. You need to go into settings and set the APN for your new carrier for data to work if the APN is not already in the phone's APN database. On a stock rom it will likely not be there. If you unlock and then flash a custom rom, the APN for most carriers will likely already be in the phone.
Finally when everyone says "oh i have a code from __________ and it took me ___ days/weeks" are the codes different? and if not.. howcome people don't post them up? (I would understand if you want to direct the answers to me privately)
Codes are unique to each and every device. They are usually based on the IMEI number alone, but in some cases they are also based on locked carrier ID and other numbers in the phone (such as an SVN number in some Motorola phones - does not apply to the Atrix or any other Moto Android phone).
Also, in the case of the Atrix 2 AT&T can and does change the unlock codes OTA once the phone is activated on their network. That is why when you get an Atrix 2 unlock code, you may receive two or three unlock codes. These are all codes that are in the databases for a specific IMEI and the wholesalers don't know which one is correct. They don't know if the original moto assigned unlock code is correct or if the AT&T one has been sent to the phone OTA. So they provide all known codes and tell you to carefully try them all. In the case of my personal Atrix 2, the first code worked and I am happily using my AT&T Atrix 2 in Thailand on DTAC getting 4G service. Once the phone is unlocked, even if AT&T sends an OTA unlock code change, it won't matter because once you unlock the phone it stays unlocked forever, unless the carrier sends an explicit re-lock command, which they
never do. You only enter the code once and it is done.
People don't post codes because they will not work on your phone. You have a limited number of attempts (usually 5 or 10) to enter the correct subsidy code. Once you have reached the limit of attempts the phone will no longer allow you to enter the code and is considered "hard-locked" to that carrier, meaning you can never unlock it by code. You will then need to have the phone hardware unlocked which is done with special software that hacks either the baseband code or NVM (non volatile memory) that is read at boot time. Hardware unlocking is dangerous and can damage your phone. Unlocking by subsidy code is the only way to safely and properly unlock your phone.
Some phones get almost instant unlock code numbers such as LG and older Motorolas as they are in databases that have been obtained by unlocking wholesalers. Some phones like very old Nokia or BlackBerry devices have calculated codes and once the algorithm is known it is just a case of computing the unlock code. Newer phones like the Atrix 2 are harder to get codes for and take two business days for the wholesalers to retrieve the codes from their source. Soon, maybe two to six months, Atrix 2 codes will likely be in the instant database and the price will drop from around $15.00 to around $2.00, but if you want your phone unlocked now I would not wait for that to occur.
Hope this answered your questions. i know I was not the intended responder but this way you get your answers faster.