There is a lot of legal misinformation in this thread, as is common on HN, both on the substance and practice-in-fact. For readers in a similar contractual pickle, take things read here with a grain of salt. Most assume very specific things about your information and bargaining position which may not apply.
In general, the applicability and effect of broad catch-all employment agreement's clauses will vary between jurisdictions - This is part of why they're drafted in a hyper-defensive manner. No small business is going to shell out for legal to obtain 300+ jurisdiction specific form agreements.
There may be very clear bright-line rules dealing with your issues as raised which put you in the clear, but you won't know unless you consult an expert. Because of the nature of the employment bar, you can get straightforward accurate advice for very little investment - if you approach obtaining advice properly.
Take the time to draft an email to local employment counsel setting out your concerns, attaching the proposed agreement and setting out the scope of review you would like him to perform. Ask for a quote. Repeat until you find a good fit.