No to both. If your tensions are well balanced, the seam is 1/4" (no slippage underneath) and the stitches are 10-12 to an inch, that seam will hold unless the fabric is too coarse, but most people don't quilt with loosely woven fabric.

I worry when I see a quilt pictured that has the tension off so the thread shows from the right side.

No, no double stitching...
I recently found one of my first quilts and nothing is wrong with it...suprisingly. I made it for my younger son before he was born, 29 years ago....and it was washed weekly for about 4 years.
This was before I knew what I was doing...so no free motion quilting.

No. Never. I do, however, reduce my stitch length to 2.

I do not sew a double stitch line, nor do I backstitch. If the pieces are smaller or being cut down to smaller pieces, I will use a smaller than normal stitch. Otherwise, all of the stitch line ends will be stitched over and secured when I put the blocks together. Once finished blocks are together and top done, I stay-stitch around the outside edge so I don't pull any seams loose while quilting. My quilting is dense enough (but never dense enough to make the quilt stiff) to secure the seams as well. I have made quite a few utility quilts for the house and those get washed often. I have never had a seam pull loose.

Double stitching would only lead to bulk in the seams. Like all the above posters who chain stitch, and lower the stitch count...that takes care of any possible issues.

If I use a small stitch length when I piece and if I have to rip out a seam it's a pain and time consuming. I like to backstitch at the start and end of each seam using a #2 stitch length. The only time I double seam is when I have a wobble in my seam and I have to make it straight.

Nope never. Only if I have a weak spot or an area of fraying - but I am pretty meticulous about removing areas or restitching so that those types of situations don't occur. I do back stitch on borders and I often use smaller stitches if I know I'm going to long arm quilt the top. :)

I don't do either. Like a lot of the posters above I do shorten my stitch length. Newer machines come preset with a larger stitch length than they used to. I.E.: The new (last 10-15 years) Berninas come with a preset stitch length of 2.5, I dial that back to a 2. I remember on my older Bernina (can't remember the model) 2 was the standard. I think that we forget sometimes that sewing machines are not built/set up for quilters, they are set up for sewers (garment/home dec). Try lowering your stich length and testing your tension (upper and lower) until you get a good stitch - just play for a little bit. If you take 2 pieces of fabric sew a line down them and then open it up you should be able to give them a tug without seeing any thread in the seam. Superior Threads I believe has some good info on tension on their website. Sorry I don't know how to explain it.

Forgot to mention, I have a quilt on my bed that I made about 15 years ago (yes it is tiime for a new one). We used to have a dog who would get on the bed a lot so it was washed once a week for many years. Now not as often but the only real wear on it is on the binding and that is mainly because my husband like to tuck it under the mattress and I like to pull on it.

Hi Ladies,
Thank you for all your answers. Looks like I may just be wasting time double stitching.
Pumpkinpatchquilter, why do you need to make a smaller stitch if it goes to the long arm?
I send my out to a longarmquilter to machine quilt. Do you machine sew them on stitch length of 2?
Thanks.