Every few years I investigate switching back to a Linux laptop. Every time I find there are still issues. Last time it was poor GPU support (no fast switching) and buggy sleep.
What issues still exist with using Linux on laptops?
It highly depends on the laptop you're talking about specifically. Some will just work, others will steal your soul with frustration. I've had very few issues on my thinkpad x240 with Kubuntu. It's an older model, but back when it was less than a year old I still had very few issues with it. Mostly with the touchpad, but that particular model is horrible even with good drivers, so I don't use it in general. I had to fiddle with some bearded parts when I wanted my battery to only charge to 70%, rather than keep a full charge while plugged in as the lenovo bits are windows only(I vaguely remember having to set up shell scripts of some sort). Bluetooth didn't work in the beginning, but upgrading to a newer Kubuntu fixed that, and I don't use that very often either, so I didn't mind. Also generally battery life is slightly worse than windows but this also varies. And although Windows 10 is a fairly snappy, it spins my fans much more than Kubuntu does.
The last computer I had significant hardware problems with on linux had a Pentium 4, but I've been vary careful with hardware choice in the last decade. Do your research and you'll be fine.
"What issues still exist with using Linux on laptops?"
It depends on laptop model, some are worse than others. Just google "<latop_name> linux problem" and see what others encounter. Personally, I don't have any problems with my 5 years old Dell laptop running Kubuntu.
I have a HP laptop for work running Ubuntu that appears on their Certified hardware list. Wifi is buggy, using an external monitor is buggy, there are always "Internal Errors", sleep simply does not work, it crashes regularly.
What issues still exist with using Linux on laptops?