The lagoon next to Maspalomas dunes is excellent. I went in June and had Whimbrel, Collared Pratincole, Kentish, Ringed and Little Ringed Plovers. Cory's Shearwaters offshore. This area is also good for introduced Waxbill and the Canary Isles Chiffchaff.
As in all dry areas, golf courses are an excellent place to look for birds, over 20 hoopoe together on the 17th hole was nice, also Southern Grey Shrike.
Blue Chaffinch exists in the pine forests but is rare and I didn't see or hear any. Canary is quite common in these areas however.
Apart from birds, there is the Gran Canaria Giant Lizard, look for this behind the chainlink fences on the roads around Maspalomas, it is quite big!
Also, be aware that there are escaped birds everywhere! Bulbuls, Glossy Starlings, all sorts of Collared type doves and stuff.