One thing I've noticed with my 2.5 year old is that, while he can count-in-sequence to 20 only missing a teen or two, he can count items only up to 3 reliably. That's because there are two ways you count items; one is where you actually iterate through the items one by one until you hit the total, and one is simply instantly recognizing a known quantity. Your brain is able to see 3 jelly beans and realize it is 3, but seeing 8 jellybeans, unless they're in a nice pattern, you probably have to count to verify.
I'm not sure if that progresses over time (ie, if a kid has a smaller number of 'recognized' counts than an adult), but it's very obvious with my son: he accurately identifies 1, 2, or 3 items instantly, while 4 he can't identify instantly, and only sometimes is willing to count them.
In terms of difficulty counting, what can be very hard is counting without replacement, to borrow a survey research term. In other words, there are 4 dogs red/blue/green/yellow, so you count, red, then blue, then green, then red, ... no, wait, we counted that one already! For a child that's extremely difficult, both because they haven't trained their short term memories well enough to actually remember which ones they've counted, and because they haven't learned pathing and sorting tricks to help (ie, count clockwise, etc.)
If you're ever in a cell biology lab, try counting red blood cells on a slide. It's nearly impossible the first time, because they're randomly distributed about the slide - pathing tricks don't work very well, and sorting is pretty hard unless you have a grid over your slide to help you out. Younger kids are basically at that level of difficulty just counting 5 or 6 dots on a die. Teaching them sorting/pathing should help a lot, but ultimately, time and practice is mostly what will help.