If your order has not been wisely routed, or it has not been wisely re-routed in response to events occuring after it was initially routed, then you can expect to sell at substantially lower prices or to buy at substantially higher prices, and you can expect to suffer drastically worse delays, and drastically increased risk that the market will run away from your order without it ever having been executed. This includes the unexecuted balance remaining after you receive a partial fill.
It is also not true that everybody can see everybody else's displayed orders. Interactive Brokers (IB) customers, for example, cannot see quotes on regional exchanges; and even if they pay for some datafeed, like E-signal, which does include regional quotes, IB customers cannot route to regional quotes (I am consdering whether to start a thread discussing regional quotes). Most retail customers see even fewer market center quotes than those customers at IB. Most retail orders are routed very poorly and stupidly (IB probably does the best job, despite omitting regionals and other flaws in its routing; and I am not aware of any retail order router as good as IB's). Many, if not most retail orders, are routed on the basis of kickbacks (called "payment for order flow", a form of fraud which the SEC legalized for the benefit of the securities industry), rather than best execution price. If you rely on orders to come to you, instead of routing your order intelligently, then you will be throwing away a great deal of money, and you will be delaying your orders unreasonably and you will suffer far more missed fills.
The following advice is highly misinformed:
If you see a bunch of prints going off at your bid price and can identify where they are executing, and you see the bid drop on that venue, it might be worthwhile to re-send your order there, but probably not.
You are almost surely better off re-routing your order in such a situation. You need to route to where the action occurs. I base this on my very careful, blow-by-blow analysis of specific orders, how they executed, and how they could have executed if they had been better routed.
Also, block trades, on the same exchange, can trade thru your order, under NYSE/AMEX exceptions to the trade-thru rule. If the amount remaining on your order is for less than 200 shares, then orders on other market centers can trade through your order (another exception). If your order is for SPY or DIA, then it can always be traded thru by up to 3 cents on any other market center, because of a special exception for those two securities. No exception to the trade-thru rule allows for trade-thrus by up to a penny; the only exceptions are 3 cents for SPY and DIA, or no exception at all.
Note that for NASDAQ-listed securities, the trade-thru rule simply does not apply at all. QQQQ lost the protection of the trade-thru rule when it moved its listing from AMEX to NASDAQ. NASDAQ has no trade-thru rule. BUT NYSE-listed and AMEX-listed securities, which are traded on NASDAQ (SuperIntermarket), are subject to the trade-thru rule, including any of their executions occurring on NASDAQ.
If your order has been routed to a NYSE/AMEX specialist, instead of a NYSE/AMEX auto-ex system, then it will receive manual execution, rather than immediate automatic NYSE/AMEX execution. Manual execution will, on average, be far slower and more costly and far less reliable than exchange auto-ex. If you cancel and re-submit, then under certain conditions (study the NYSE and AMEX rules), you will be able to receive immediate automatic execution, at a better price than you would receive if you simply waited for pending manual execution. Sometimes, cancel and resubmission can get you an execution which you would otherwise not get at all. It might be an even better strategy to avoid execution by specialists entirely, unless you have a strategy that allows you to profit from your insight into how specialist's behave.
And yes, routing of equity orders is a pain in the butt. Correct routing is absolutely critical to minimizing trading costs, delays, and missed fills. Stupid order routing will greatly increase your trading costs and delays. Missed fills have an even worse consequence. The missed fills resulting from stupid routing will cause you to tend to receive fills at those times when your trading strategy is wrong (market moving \against you), and to miss fills when your trading strategy is right (market moving in favor of your strategy); so that you will suffer reduced profits and increased losses even on a gross basis, that is, while ignoring commmissions, spreads, slippage, and other trading costs. Stupidly missed fills will damage your underlying trading strategy, by reducing your gross profits, even before we get to the point of considering your net gain after trading costs.
Also note that cross trades, on NYSE and AMEX, receive higher priority than orders submitted prior to the orders resulting in the cross trade.
Also note that on AMEX and NYSE, time priority is lost, and your order is put on parity with more recently submitted orders, and often (see NYSE/AMEX rules) your order is put BEHIND more recently submitted larger size orders, whenever a trade simultaneously exhausts all shares on both the bid and the ask. This is very different from ECNs, where strict price-time priority is persistent, rather than fleeting, and therefore plays a far more important role, and larger size orders cannot jump in front of newer, smaller size orders, as they often can on NYSE or AMEX (see the rules for details). Many traders do not realize the very limited role played by time priority on NYSE and AMEX, and that order size plays an important role in determining priority on NYSE and AMEX.