I'm a late bloomer and didn't join a basement jam until I was 50 and I played my first show in a gigging band when I was 54, so I'm always the least experienced person I play with. By a lot. I don't have the advantage of having learned when my brain was young and sponge-like and then had decades of experience to be able to just feel where we are in a song and create magic. For me, I find that I have to stay sharply focused on that balance between "being in the moment" while still paying close attention..........
^^^I had to scroll back up and make sure that I didn't post this, at least the first half. Some good stuff there.
I have been playing for 14 years now, started at 50. Started singing 3 years ago. They made me. Doing both is hard; but I figure that's just age and I learn slower. Lots of mistakes early on. To make matters worse I'm starting to play a keyboard with bass while playing other parts, like piano or horn tones, while singing. A glutton for punishment, I suppose, but it's fun and challenging. And a lot of work.
I see a lot of really good advice here so far; and some pretty bad stuff, too, frankly. For what it's worth, you have a few very specific things that are happening. I think you have to figure out exactly what they are and precisely when they occur. Because it's
not all of the time. And then address that/those specific issue(s). General solutions sound great, but don't usually address specific problems. If they are something practice can't fix, no amount of practicing will help.
I'd get verse order mixed up, or sing lines from other verses. It would be fine in practice, so more practice, the brute force method, wasn't the answer. Understanding the story and learning to tell it accurately was, because then the order of all the lines made sense. Music is just telling a story, right?
I couldn't do running 8s while singing, especially verses, they'd get sloppy and sporadic. I dropped to quarter notes. The guys didn't care, heck, they suggested it. Nobody noticed. Doing 8s during the choruses and leads made those stand out more, so our dynamics were enhanced. The problem instantly went away after one time through the song.
One more, a specific singing issue; leading lyrics, I believe they're called. Lyrics that start before a downbeat. Or conversely you could say the line starts on the last 3 or the 4 beat of the previous bar. I tried to think of them as being part of the end of that previous bar; didn't help a bit. I practiced. A lot. Ha.. I finally figuring out that one of the words coincided with the ensuing 1 beat worked. Just getting the lead-in words done before that word made sense, just like making sure your riffs are out of the way before you hit Bootsie's "The One". I'm still working on it, but I know specifically what to do.
Not that I don't have other issues, but these specific solutions to specific ones worked out.
BONUS TIP: for singing and playing: Consonants are the beats, vowels are the notes. And the beats can come mid-word. I highlight the specific letters on my lyrics sheets and they're a bright yellow on my tablet. It helped my singing a LOT.