I can't remember if I took my synthroid pill this morning... should I take it possibly again? Is it better to skip a dose accidentally than take a double dose?
Probably best to skip. Your levels won't drop that much skipping one daily dose and you will probably experience no bad effects. You don't want to overdose though.
You can take it again as long as your regular dose is not at the high end (TSH suppression therapy) or you can skip.
If you double dose with T4, one day will not harm you because the half-life is 7 days, it may increase metabolism and clearance of T4, and your T4 to T3 conversion or CNS T4 transport will be downregulated. These are protective, compensatory mechanisms so that your heart is not exposed to excess T3.
I accidently overdosed on T4 for a week before I noticed that I was taking it from the wrong bottle (3x higher dose) and felt fine until the 7th day of overdose when I realized the mistake and started to feel agitated. My labwork was only slightly elevated and stopping the medication for 3 days was all that was needed.
I am on TSH suppression therapy. I am having trouble keeping my TSH down lately... so skipping is not so great for me.
But so far, I did not take another pill because I have high blood pressure and don't want to make my heart race... 
I am usually very careful taking the pill but this morning was chaotic.