I would start by thinking ahead of your son.... ie, if you know he likes to spill the water bowl then move it to an area that your child doesn't have access to or put up a baby gate to block him from the kitchen. You can NOT expect that your 14 month old can even begin to understand why it matters that he dumps the water or pulls the cords....infants/toddlers have nowhere near the logic or reasoning capabilities as an older child or adult and can not be expected to understand. Time outs for a 1 yr old are not worthwhile....they do not have the thinking capacity to put it together....especially if you want to use the playpen for other uses.
As a biologist and animal trainer that has read many, many books on both human and animal behavior, the other mom was absolutley right that you can be proactive and help teach your child what you would prefer they be doing without yelling, hitting, punishing or being physical at all....it's all in how you set up the environment for success and give him lots of attention for the behaviors that you want. You have to set up the house for success....remove the water bowl, pull up the blinds, get a cord/outlet cover for the water cooler plug, repeatedly demonstrate and encourage proper petting of the dog (and give the dog a safe place to go where the baby can not get to, ALWAYS)....
These are all normal behaviors for a 1 yr old, nothing that needs to be punished for, but all that need to have mom/dad avoid...
As for the head-butting and biting, try to be proactive in what situations and energy levels prompt it and try to avoid it, if he does it, put him down and remove all attention from him.... he loses cuddle time, being held, etc by hurting....it is a stage, it will pass, but remove yourself so it only happens once her episode and try to minimize the occurances by seeing them coming.
Just remember, your little guy is totally normal. Maybe he needs his toys rotated to draw attention to them more? Maybe more one on one play and attention time? If he's busy playing with you with his toys, blocks, cars, puzzles, he can't be dumping the water bowl at the same time....if he has to be in the kitchen for a short time while you cook, etc just take up the bowl :-) Hang in there and enjoy your little one and remember this is all part of him growing up and exploring and discovering....