The unfortunate reality is that there is a double-standard in business with regards to job seekers compared to how those involved in hiring are evaluated.
From the hiring perspective, there are usually tremendous numbers of prospective candidates. Their initial task is to shrink that pool of candidates to something more manageable. Strategies for accomplishing this include hiring a recruiter to handle much of the workload, and working off of a list of "automatic disqualifications". What those automatic disqualifications may be vary from hiring personnel to hiring personnel, but spelling and grammatical errors are frequently on that list because it is simply easy to spot.
The recruiter, therefore, has less incentive (i.e. none whatsoever) to take extra care with their spelling and grammar when communicating to prospective recruits.
If they made similar errors when communicating with the hiring managers, that might be a bit more concerning, but you, as a prospective recruit, will be unlikely to see those correspondences until much later in the process, if at all.
Remember: you are probably not the recruiter's customer.
In many cases, recruiters represent a specific company looking to fill a position, which is their customer. Other recruiters work differently, and try to establish relationships with talent so that they can keep them on hand for a variety of prospective jobs. These latter types of recruiters are generally much better to work with (imho), but I still wouldn't consider spelling or grammar errors to be a red flag.
Even if the hiring manager makes spelling and/or grammar errors, I wouldn't be too concerned. The pressure to be formal and precise simply does not exist for them the way that it does for potential hires.