Having run stable 13-player groups (with everyone showing up every week, no less) in several systems, a large group has 4 issues:
1) face time for every player
2) Synergy of group size.
3) Appropriate challenges for the group as a whole
4) GM communications
1 Face Time
Now, my big group for D&D3.X was 9 players, not 13, but finding challenges (especially given the average level was 10th) was minor compared to just making certain every player got some face time twice or more every session. That was handled best by simply having NPC's target different PC's for their interactions; in other words, not leaving it to the players to decide who interacts with a given NPC.
The synergy effect comes from overlapping skills and the help rules. Which said, the help rules in 3.x are pretty weak, but they do add up. Further, with large groups in 3.X, you'll tend to get more over-the-top combat potential due to players having similar roles.
The challenge issue is an evolution of the synergy issue. Remember - not every monster is intended to be the "ideal party" challenge; many are really balanced for an ideal party but are taken out mostly by one member of said party, often the wizard or the fighter. (Keeping in mind: ideal party is 1 fighter, 1 wizard or sorcerer, 1 cleric, and 1 rogue.) Most are fighter based - and my experience is that large parties tend to be heavy on fighters and wizards, light on rogues and clerics, and having few of anything else. So, often, combats will depend on how competent the targeted players are.
Further, fights with a few large monsters tend to become very one-sided when the first big-bad goes down, as those resources fighting it get diverted to the others. That's normal; it's just more obvious in larger groups.
Some specific cases to remember:
Undead: aimed at clerics, especially the incorporeal ones. Balance the encounter based upon the party being the level of your clerics, and sized at 4x your number of clerics. Simpler undead, like skeletons, who present no conversion issues, can be used to protect the higher level undead from turning, but also can be taken out by fighters and combat wizards easily.
Incorporeal anything: clerics and wizards - the fighters are close to useless. For large groups, always give the fighters something to face that's corporeal.
potent monsters: many monsters are highly potent - some surprisingly so - such as Illithids and Beholders. Don't add more to balance them; add subservient fighters instead. Beholders, for example, should usually be solitary - to buff it up, add enslaved kobolds or orcs, or a couple lucky rounds will be a snowball effect.
4 Communication with the GM
The solutions vary by group, but mostly break down to turn taking or collating. Usually in some combination. Some additional options
4a Collating Actions
By collating, this means a small number of players talk to the GM, but tell the GM what their and several other players' characters are doing; it is a variation on the single "caller" of AD&D rules fame.
The classic solution was to run the game as a minis wargame, with ONE player collecting/collating everyone's actions. It works, but it can be unsatisfying. It is, however, how E. Gary Gygax ran parties of up to 20 players.
4b Turn Taking
Simply make certain that turn taking isn't just in combat. When it comes time to get actions, go around and pointedly ask each player for what they're doing. Much above 5 players, the traditional popcorning of actions no longer is viable, as the noise it generates becomes considerable, and too much gets missed.
A Harlequin is a player who plays only NPCs. They don't narrate, don't resolve game rules, and don't get special authority. They are a real challenge for some groups, but in larger groups can be spectacularly successful at reducing the GM overload.
This is especially true in certain types of play. For example, in one large (13 player, 25 PC), I had a 14th player who couldn't show regularly. When he did, he got to play NPC's. If he was negotiating with the players, I'd give him a list of what his allowed resources were, and turn him loose with the away team sent to deal with him. Meanwhile, I'd do the GM-needed interactions to solve the overlapping mechanical problem of the week. And when done, he'd note down the final resolved issue.
Further, Harlequins allow the GM to have really GOOD dialogue from multiple NPC's.
The drawbacks are that many can't make the distinction between assistant GM and Harlequin. It can be set onto a continuum, where certain situations the harlequin is allowed to call for certain rolls, and that works, but once they start calling for rolls for anything other than affecting the character they play, they're really into being assistant GM's.
4d Assistant GM's
The problem with an assistant GM is trust. You HAVE to trust them not to muck up your adventure. The benefit is that you don't have to run the whole group all the time, and if the party splits, you take one part and they take the other.
Assistant GM's are best made from harlequins, not experienced GM's. Start letting the harlequin players call for rolls, and slowly build them up to being part of the resolution in general.
It's very important not to have the assistant GM's contradict your calls, but likewise, if it's not a rules issue, if they make a call, back it up.
5 Problem Players
Some types of players tend to be problems in certain groups... the classics being Rules Lawyers, Attention Hounds, and Shy Guys.
5A The Rules Lawyer
Co-opting the rules lawyer to assistant GM is great in minis-mode, not so good in story mode. Leave him/her as a normal player, but ask them for advice on rules issues. Don't make them officially assistant GM's.
5b The Attention Hound
The Attention Hound really works well as a harlequin. It puts him in the center of things, but also keeps him from eating your time as GM.
5c The Shy Guy
This is the guy who shows up, but doesn't really speak up. The kind who act only when asked, "What's your character doing?"
The shy guy, in a small group, can be coaxed by the GM into playing. In a large group, they often fall by the wayside. The trick is often to have another player prompt them; in some cases, having them be the caller for a small portion of the group can break them out of their hesitance.