Ah, the Dreaded DM PC, creature of legend and horror. There are ways to do this in a way to not cause problems, but it takes a disciplined DM to pull it off. Honestly, the only thing harder to do is DM your significant other... while keeping them your significant other! Basically you need to keep them from being a font of information, except when necessary (often to get the adventure back on track), and you cannot show favoritism (if anything, show the opposite).
What I mean is a frequently used NPC that either is an ally or even a member of the party. Obviously it is just an NPC, although if it is a multi-DM campaign, I suppose it could also be the DM's PC when they play. In the past I have sometimes used such an NPC, whether to flesh out party ranks, to be a source of information or guidance in some way, or just add a bit of regular interaction.
How have you done this? Again, I'm not talking about the countless NPCs - even frequent contacts - that the PCs will encounter, but one that is either a member of the party, or perhaps regularly drops in and out of contact. Are they just another party member or do you use them as a source of info dumping when necessary (e.g. Gandalf), or somewhere in-between? What problems have arisen? Etc.
My very first game had DM PCs; I mean a LOT of them. The DM had over 100 characters he'd played to various levels, but that wasn't too uncommon back in the day (early 1E). He primarily used them to fill out groups where there weren't enough players. He'd also allow a player whose character died to play one of them until the end of the adventure, and if the player like it, he'd turn it over permanently (helping players not have to start over at level 1 again). In this way his DM PCs were great, but he had favorites that were never available for players to use, and "somehow" always got the best items. Whenever one of those characters joined the adventure, we knew it was going to suck.
In another RPG, every GM had a GM PC because we all loved the setting and wanted a character able to impact it. Eventually I became the permanent GM, and limited my use of GM PCs. During certain "classic" campaigns, the players expected me to play one of my iconic characters (we each had an ideal persona that we wished we were within the setting). Eventually I decided to use this to my advantage and made my character the focal point of the entire campaign... by making him the focal point of EVERY single plot hook (his life was a walking disaster). Eventually the players wondered why everything bad seemed to happen to him, and I let them eventually divine that he was cursed. The campaign ended with the players freeing him from the curse, allowing their friend to return to a normal life.
Interestingly I find the concept between an NPC and a DM PC eventually blur. In my first 5E campaign, the party eventually rescued an elven ranger who was part of the first group to attempt the adventure. The original 1E adventure had her with full PC build (as it was in 1E), and nothing in the NPCs of the MM came close to what I needed. I decided to then stat her out like a PC, about 3 levels below the rest of the party. During that adventure, I decided to have her fall in love with a PC's elf eldritch knight (closest to a bladesinger we had), so she kept finding reasons to stay with the party. At a later adventure, the party was trapped in a secret hallway between two areas patrolled by giants looking for them. Because the giant king would know about the secret hallway when he returned, they knew they had to escape quickly. I had the NPC offer to go out one of the doors, distract the guards, then run back into the hallway, catching up to the party (that had already run out the other end). She was the fastest, and it was a solid plan... except she rolled a 1 on her Stealth check. The giants pounded her to death in one round, causing the players to attack with reckless abandon. I was astounded at this reckless plan, because they seemed more focused at getting to her than killing the giants. During the battle, the paladin eventually got to her and cast Revivify, which was their entire plan! They considered her my DM PC, even though she was just an NPC to me, and treated her the same as they would any of their character.