The main thing is that when ironing synthetic threads, you need to use a lower temperature and always place gauze or a special mesh between the fabric and the iron's sole plate. Synthetic material really does melt at high temperatures, and black spots are burnt thread remnants. It's a normal problem, but it's easy to avoid - just regulate the heat.
Try checking the care label first - if the item is made of synthetics, you should iron it on a gentle setting altogether. If the stitching is embroidered on top of natural fabric, set your iron to the synthetic or cotton setting on the gentlest option, not on maximum. And never press the iron down for too long in one spot, especially if there's a concentration of threads there.
For these kinds of items you can actually skip ironing entirely - many modern synthetic fabrics hold their shape well. If you really need it perfectly smooth, lay down a damp cloth, heat on the lowest setting, and run the iron more lightly, more like touching than pressing 😊