I agree- keep him on leash, don't go to the dog park anymore, and be weary when around other dogs. I also agree prey drive might be to blame with his attitude to smaller dogs, in which case you want to be very careful. Aggression/fear/anxiety/poor social skills are things that can be trained out, but prey drive is much harder to train against.
Also be aware that tail wagging really just means a dog is excited/aroused- it doesn't mean they're having a good time, are going to be friendly, are happy, or that they're not about to try to attack. Dogs will literally try to kill each other while their tails are wagging, it isn't inherently a reflection of emotional state. Dogs will usually have different ways they wag their tail that do point to possible emotional state- tense, tall body, stiff tail moving side to side may be an indication of discomfort/anxiety/a warning, while a dog who is wagging their entire butt and is super wiggly looking is probably friendly.
This is something that it might be a good idea to consult with a trainer about. It's still fairly managable, he's not lunging or barking, but he definitely is showing he has some issues with other dogs. From an internet post, it's hard to tell what the root of those issues are. It could be fear, anxiety, poor social skills, he might just be uncomfortable with strange dogs being very close to him, or it could be something else. IMO the underlying emotional state that leads to dog aggression is important in deciding the best course of behavioral modification and something that should be addressed, but really can only be determined by an in person evaluation.
Dalmatians do often have issues with other dogs, IME- they're not the easiest breed to live with, usually, and when not well socialized as pups (see below) they tend to have issues with interacting well with others.
I terms of what you can do on your own, I'd suggest reading up a little bit on general dog behavior, social skills, play behavior, and behavioral modification for aggression/reactivity towards other dogs. By no means do you need to be an expert, but its always a good idea to have an independent understanding of a dog's issues so that you aren't just blindly following the advice of a trainer, which may or may not actually be good advice. There are a lot of dog trainers out there. If you choose to work with one, look for someone who is CPDT-KA, belongs to APDT, and/or is a certified Behaviorist through the IAABC, Animal Behavior Society, or ACVB. Those are all good indications that the person knows what they're doing. Anyone can call themselves a dog trainer, so its important to find someone who has both knowledge and experience.
In terms of behavioral modification stuff to look into, teaching an attention cue for the dog to look at you is universally a good idea, because he can't react to the other dog is he's locked on eye contact with you. The "Look At That" game is another thing you might try, but would probably be easier to teach him if you have a trainer helping you just because its a little more tricky. Behavioral Adjustment Training (BAT) and Desensitization/Counter Conditioning are also commonly used, effective methods.
A good description of training attention (note: you HAVE to work on this away from other dogs first before the cue will be strong enough for the dog to actually look away from the approaching dog; it will take time and can be frustrating): https://positively.com/dog-behavior/basic-cues/watch-me/
"Look At That" game: https://clickerleash.wordpress.com/...itive-approach-to-dealing-with-reactive-dogs/
B.A.T: BAT 2.0 Overview | Grisha Stewart
Counter Conditioning/Desensitization: Desensitizing and Counter-Conditioning: Overcoming Your Dog?s Issues
A few really good on-line resources:
Barking & growling, signs that trouble is brewing | Trisha McConnell | McConnell Publishing Inc.
Dog-Dog Reactivity – Treatment Summary
Dog-Dog Reactivity II — The Basics
Aggression and Reactivity Training | Karen Pryor Clicker Training
(I've only ever read this article from this site, so don't know if they're all good info, but i like this article): Gaining Focus: Building Attention with a Reactive Dog
Good behaviorists/trainers to look into are Ian Dunbar, Patricia Mcconnell, Sophia Yin, Karen Pryor, Jane Killion (who has a GREAT book about training unmotivated/non-biddable dogs that don't care what you want called "When Pigs Fly: Training the Impossible Dog"), as well as Grisha Stewert.
Finally, you might be well served by reading a few books about reactive dogs, ESPECIALLY if you don't have the money to work with a professional. "Fight!" by Jean Donaldson, "Click to Calm", and "Feisty Feido" are all great books dealing with reactivity.
Also, I would suggest working on recall ("come"). I would use a long line to work on this cue.
With a Dal, I'd be hesitant to use any kind of aversive/correction based training methods. These can (not always, but can) cause things like escalation, redirection of aggression, and/or cause the dog to shut down (esentially learn they can't escape the thing that they don't like, like other dogs, and that reacting in any way causes them discomfort, and so they just sort of give up- often looking like they're "fixed", but really just being so stresssed out they can't function). Given my limited experience with Dalmatians, I would say they're a breed I would consider more likely to respond to a correction with aggression of their own than say a Pit- which is more likely to just ignore it- or a Lab- which is more likely to be like "huh, I didn't like that, maybe I'll stop doing this".
A note on socialization: socialization is very important, but it is much harder to socialize a dog after puppyhood and the critical periods of socialization that occur during their younger months. From around 6 to 16 weeks, puppies go through a critical period of socialization. During this time they are especially imprint-able and this is the time when they need to learn how hard is OK to bite, what is ok to bite (ie, dogs are OK, not humans), how to interact nicely with dogs (they will do a lot of lunging and biting and holding at this age, which well socialized older dogs are able to tell them not to do by growls and light nips to tell them to bugger off), and how to play and when play becomes too rough. Pups also go through a fear period at 8-11 weeks and again at around 4 to 8 months. This is a good overview of what the critical periods are, when they happen, and what they mean. Note that the use of the term "dominance" is more to do with the idea that the puppy will begin to exert its own control on its environment and not the way dominance theory trainers use it, to mean the dog wants to become "alpha" or top dog. Dogs are not status seeking animals, for the most part.
CRITICAL PERIODS IN A DOG
When people talk about socializing your dog, they usually mean it in terms of these critical periods. Puppies are set up to learn about the world and the rules of humans and dogs in a safe way- until adolescence puppies will have what behaviorists refer to as a "puppy license" meaning that they can get fairly rough and inappropriate while they're learning and (well socialized, socially normal) adult dogs will still be gentle in their corrections to them and will be very unlikely to actually hurt them. Unfortunately, this changes around adolescence as sex hormones kick in and dogs get larger, and adult dogs will start to become more severe in their corrections to the puppies, sometimes displaying aggression more than a patient "hey don't do that". When an adult dog comes bounding over, head-on, and jumps on another adult dog, that is likely to be met with some kind of aggression, whereas if a puppy did that the adult might just lift a lip and move away. When trying to socialize/teach social skills to an adult dog, you have to be careful of what dogs you choose to allow them to interact with, because many will start getting aggressive if the unsocialized dog acts inappropriately (ex: excessive humping, tense body language, biting too hard, etc). This means letting them play with unknown/strange dogs is risky, and a dog park is the very worst place you can bring a poorly socialized adult dog. Dogs are penned in with each other and may or may not enjoy being there, are likely a little bit stressed and on edge, and oftentimes people will bring their outright aggressive dogs to the park because they don't realize that they're aggressive and not just too rough.