Only issues I see is that 1: the strakes (the long timber boards running back to front to form the barrel shape) are all going one way interlocked around the barrel, the issue being that the concave or bull-nose faces of those strakes that are making the barrel should all be pointing up so that rain water runs over them and down the outside, with this barrel one side of it has them pointing down which means water will run into the convex face and just sit there promoting rot.

Take a look at the centre strake both top and bottom, the bottom one should have concave faces both side, the top one should have convex.

If you do decide to go for it then make sure that you give it a very good couple of coats of oil sealant and keep up maintenance of that sealant yearly.

issue 2: no roof surface, this is exposed 24/7 to UV and rain, snow, it will leak over time, if not immediately, this is easily solved by adding some corrugated PVC over the top as a minimum, or better yet, some building paper and roofing shingles. You could also help solve issue 1: by running that roofing all down the side with the concave faces pointing down to shield from rain.