Playtesting is something I've mentioned in other posts previously. This is a consolidation and expansion of those thoughts, things I've learned through play testing our Network rules. This is simply what works for me and what I believe will work for the typical gamer, I am sure other people have different experiences though.
Here is what I've found helpful:
Crunch the numbers
This just boils down to doing the math and making spread sheets. Probabilities are really important in an RPG. You can develop an intuitive sense of them from just playing the game a lot but it is still critical to know the actual numbers. If you make an injury mechanic for example that is triggered by a critical result, you ought to know the likelihood of that coming up on a given roll. With single dice systems this can be relatively easy to calculate (a 20 comes up 5% of the time on a d20 roll for example), with a dice pool (which is what I tend to work with) the probabilities are a lot more involved and you need to hash out all the potential pools a player or NPC might have..
For instance in the Network system the Target Number and the dice pool can vary. This creates a certain level of opaqueness, which I like on the player end but isn't particularly good on the development end of things. So we created charts for ourselves that show the probability for different skill ranks and modifiers against all the possible TNs. With this we can see what 2d10 against TN 8 is but also see what 5d10 against TN 6 or TN 9 is. Without this we would have been working in the dark.
All that said, even if you have the probabilities mapped, and you know the numbers, you still need to see it in play. The math can give you a clue, but it can't give you the experience itself.
Play your own games
I think this is one of the most important things in play testing and development. After you finish your game and publish it, you should keep playing it. Otherwise you start to know less about the system than the fans and it becomes increasingly difficult for you to write and design support material.
This may mean some sacrifices on your end. Campaigns are time consuming. Most people can only manage one or two sessions once every week or every other week. If you have the extra time you might be able to squeeze in more. Ultimately if you have to choose between running your own game and running the latest edition of D&D, I think you should choose your own. If you'd rather play D&D, you might want to consider making d20 material instead of using your own system.
Play other peoples games
I do think it is important to play your own system. That said exposure to other games is also important. This can be hard if you are busy running your own system. My solution is to be a player in games with other systems and to focus on GMing my own games. I also run one-shots of systems I am interested in (but nothing beats long term play over time). In addition to these solutions one thing I've tried from time to time was setting aside one sunday every week or couple of weeks to run a different system. Usually I do this sort of thing when there is a block of games I want to try out and consider for longer term campaigns.
Run focused play tests
These are sessions where you hone in on specific parts of the system. They are not about running through scenarios or a campaign, rather the focus is putting individual mechanics to the test. In this kind of session you might run a bunch of characters against a single set of challenges and one combat encounter, you could focus entirely on combat, or traps, or poisoning. Whatever mechanic (s) you feel you need to see in action and evaluate, you can run it through a bunch of different but similar situations to get a handle on.
Focused platests in my experience are necessary though they are not as enjoyable as just running a regular adventure. With focused play tests it helps to stay organized. Take active notes and put together spreadsheets to gather data.
The value of the focused playtest is it forces a mechanic into action so you understand it, see some of its flaws and can get a better handle on its overall level of balance in the game. It can also help you uncover anything unusual you might not immediately see just reading the rule. For example your poison mechanic might break down under scrutiny, perhaps it just doesn't connect well with the act of poisoning a character in game (too abstract or just not thought through). A focused playtest can help you see this.
A downside of the focused playtest is it can lack the context of the full adventure or campaign. That can create problems for evaluating balance because none of your mechanics are going to exist in a vacuum. Something that seems broken in an isolated encounter or challenge may not be when characters are trying to use it over the course of a regular day in their life.
Run full campaigns
I am a big believer in running several campaigns of a game while play testing it. These can be run at the same time (which I find gives you a big window into the system) or back to back. There really is no replacement for a campaign when trying to crack a system. Things just come up over the course of campaign play that don't in limited scenarios or single adventures.
Honestly this is the most helpful thing I do during play testing. There is nothing quite like running a campaign to get a handle on what your system does well, what the strengths of the setting are, and how everything just comes together. The worst place do figure all that out is in your own head, the best is at the table.
If I didn't run campaigns with my own games, I don't think I could even begin to write the GM section of each book. I just don't see how you do that if you haven't run an ongoing campaign of the system and setting.
Don't be the smartest person in the room
There is a temptation when GMing and when designing a game to be smart, not to allow people to catch you being stupid or making mistakes. If you made an error in the game and it comes up in playtest, accept it, acknowledge it. You will make mistakes. You will make stupid decisions. There will be inconsistencies. When people point these things out, that is good, it means you are finding the problems that need to be fixed. If you let your ego get in the way that can hinder the process. Your job isn't to be the most brilliant thing at the table, your job is to get feedback from people who catch your mistakes.
Take notes for everything. You can playtest 1,000 hours for 41 days and nights, but if fail to take notes, most of your observations will be forgotten or misremembered. As a general rule, write down observations the moment they come up.