1) Welcome to the Party!
2) As you are obviously new here, I have some suggestions to help us all help you:
When you post, please post your entire configuration including (but not limited to) your installation method (7.X.X?) and vicidial version with build (VERSION: 2.X-XXXx ... BUILD: #####-####).
This IS a requirement for posting along with reading the stickies (at the top of each forum) and the manager's manual (available on EFLO.net, both free and paid versions)
You should also post: Asterisk version, telephony hardware (model number is helpful here), cluster information if you have one, and whether any other software is installed in the box. If your installation method is "manual/from scratch" you must post your operating system with version (and the .iso version from which you installed your original operating system) plus a link to the installation instructions you used. If your installation is "Hosted" list the site name of the host.
If this is a "Cloud" or "Virtual" server, please note the technology involved along with the version of that techology (ie: VMware Server Version 2.0.2). If it is not, merely stating the Motherboard model # and CPU would be helpful.
Similar to This:
Vicibox X.X from .iso | Vicidial X.X.X-XXX Build XXXXXX-XXXX | Asterisk X.X.X | Single Server | No Digium/Sangoma Hardware | No Extra Software After Installation | Intel DG35EC | Core2Quad Q6600
3) Timing devices are not necessary, usually, but sound quality is often heavily dependent upon the sound card in the agent's workstation. If you are using different workstations with different sound cards and some have USB and some have IP phones, it's unlikely that "all" would be poor quality, although still possible. If all your agents have the cheapest workstations you could get your hands on, and the cheapest headsets as well, that could certainly be your issue. Get a couple USB headsets to see if you can improve quality.
4) PRI: This is technically defined as "part phone part internet leased connection". But does not specify whether these are PSTN/T1 telephone channels or SIP channels over the internet portion of the PRI. If this is PSTN over T1, all the hardware involved must be checked. The card in the server, any channelbanks involved, the T1/PRI interface box provided ... any/all of them could be the problem.
5) Many call centers with limited bandwidth will use a colocation facility for their Vicidial server and that way only need enough bandwidth to get their agents to the server's location, thus reducing their need for bandwidth (often down to 50% or less). If the problem was with bandwidth, this can remove the problem completely. This costs extra money, if course, since you now are paying for colocation ... but if you do not have fiber or "lots of bandwidth" available, it's often the only viable option. Then the challenge is that you will need to break your lease with the T1 provider, and they are often still just as bad as AT&T in the 70s (will rip you off at every turn, and try to lock you into a contract with systems that don't even work as promised).
4) This is not a "General Discussion". It's a request for support. Moving to the proper board accordingly.
Happy Hunting!