1) In our backyard we recently built a flagstone patio on a concrete base.

2) Patio length is 25 ft from the back walls.
3) We had two water sprouts that got buried below the stone patio and draining water out well beyond the patio perimeters
4) Patio is built on pretty good gradient level (Our backyard has a good slope). Patio has a seating wall on the far end of the patio.
5) There is small water pipe (half inch) through the seating wall to drain out water from the patio surface
5) We are in the process of making flower beds just on the perimeter on the far end the patio just behind the seating wall.
6) As we were digging, after about 1 1/2 feet, I saw water oozing out and filling half feet up the hole. Day before digging we had heavy rains in the area and soil is very clay.
7) I emptied the water from the hole and went back to see it. Again I saw half feet of water. I emptied the water again.
8) I repeated this 5 or 6 times and probably have emptied about 10 gallons of water.
10) Right above the place where I dug, the patio water gets drained out via a half inch pipe.
11) I dug another hole 4 feet away from first hole and I did not see any water. Second hole is slight on a upper slope.
12) Also We don't have any water lines in our backyard

Should I be concerned with this water getting filled up in the whole?
Will it cause any future drainage issues?
Any possible damage to the patio?
Is it a good idea to put plants in that area?

Please let me know your suggestions.

Thanks
-Pradeep

A couple of ideas come to mind: you might look into extending the drain pipes so the water drains to an area where it doesn't create problems. Or you might look into creating a French drain. You could Google these ideas online and see if they make sense for you.